The possibility of Roundup has interested me for quite a while. I made some rules for in in the game Liberty Roads (
http://talk.consimworld.com/WebX?8@@.1dd317cd - post 1918) that I finally got around to posting. It doesn't necessarily present the most optimal invasion or response or even the most plausible scenario (which I'm increasingly convinced is an invasion in May or June), but the system is quite nice for actually gaming out the result and can readily adapted to other situations.
I support the notion that a 1943 invasion would result in faster defeat of Germany. In general, I don't think there would be any huge setbacks for the Allies (though probably some nasty Salerno/Bulge-like costly victories). Thus, the general principle of bringing more available combat power (which is concentrated in ground forces) to bear on the enemy in a better arena (the plains of France versus the mountains of Italy) would be the key factor in expediting the German defeat.
Regarding amphibious shipping, the Allies were able to bring in many divisions in Sicily in 1943, just like Overlord the next year. Thus, the initial invasion would be approximately the size of Overlord. This is easily enough to establish a beachhead in Normandy or even Calais. However, the lack of shipping would reduce follow-on forces compared to Overlord in 1944. It was be easier than Italy, where multiple invasions took place further from Allied logistical centers, but still less than 1944. No doubt the Allies could reduce north/south Pacific operations to get some additional life compared to historical 1943 Europe, though. They could also add a bit more amphibious shipping to their built schedule with a firm commitment in mid 1942, though this would likely be small due to the perceived need to build more antisubmarine forces.
The submarine menace was not a big deal by May 1943, in terms of ultimate outcomes. It never interfered with troop transports, at any rate. It would certainly make Roundup appear like more of a gamble to planners in 1942, but arguments could go either way, especially with an analysis in 1942 indicated that the menace could be resolved. Regarding Bolero, there might be less stuff available in the UK, but that may not slow things down much if there is not enough amphibious shipping to move them anyway. In Overlord, many US divisions came from the UK, but tons of logistic support came directly from the continental United States. Even if only the initial landing and followup forces were in the UK from mini-Bolero, the campaign could still be conducted with shipping form the US coming in at the maximum rate that French ports could handle. At the big conferences, lots of people had opinions on things, but I think it was rare that people actually sat down and crunched numbers for different variants. The conferences could also get very political. Thus, I would put much weight on what any of them say at any given time. This applies to commanders and political leaders that were optimistic OR pessimistic about Roundup. All their proceedings are of course very historically important, but humans are far to complicated for us to just identify prominant figures and take their opinions at face value. Warfare is complicated, and there is a lot that they didn't know. I expect that even with a January 1943 decision, there could have been a strong Roundup (though obviously a commitment earlier would be better since it would allow proper coordination with Torch and PLUTO construction).
The Luftwaffe would certainly be more dangerous than in 1944, but I can't see it being even as bad as Italy in 1943, where the Luftwaffe achieved some notable successes. Even in Italy, the Luftwaffe did not have a large impact, though. In Roundup, Allied fighters would be closer to their main bases than the Luftwaffe (Luftwaffe would be closer than in Italy, but the Allies get a bigger advantage here). There would also be a lot more of them. It doesn't matter if the Luftwaffe has a temporary qualitative advantage. The odds in the air are simply better than historical for 1943 because of better basing, and the Luftwaffe still lost in 1943. It would be even better for the Allies, since the invasion would result in heavy bombers doing fewer longer range missions into Germany where they were unescorted. Thus, the Luftwaffe would be depleted more quickly than historically, even though they would do somewhat more damage than in 1944. Even more so since by winter, most of France would be occupied, giving Allied bomber many more protected routes into Germany
As others have noted, both the US and Britain did not do a good job of getting lessons learned to green divisions. The Allies would probably still suffer a bit from not having gotten rid of bad generals in 1943. Still, there would be no great change in performance. At the tactical level, the Allied tanks would better stack against German tanks. The Germans would still have a little more of a tactical edge than in 1944, though, because of lower reductions in manpower. However, their industry had not yet reached the peak. Thus, the initial "odds" of the Allies would be lower after the Germans brought in sufficient forces from Russia to stabilize the line, but the German replacement rate would be lower than 1944. Further, the Allies would soon be able to bring in new forces nearly as quickly as in 1944 after they capture some ports and need to rely less on amphibious shipping. Thus, the overall balance of power would move more quickly in favor of the Allies on average than Overlord.
I don't think the Allies could politically abandon lend lease, though I can certainly see the increase in lend-lease slowed down compared to historically. Additionally, the Soviet Union would be able to advance more quickly than historically, even received less lend lease. They would still have obtained many trucks, and it is much easier to advance an army when there is less opposition. Opposition is part of the difficulty of logistics (bullets, shells, and equipment needs to be moved just as much as gas). The Germans would certainly use the room in the east to retreat after having moved more forces to the west, which is in more immediate danger, though there would be limits (both political and practical) on how far this could go. Thus, it is likely overoptimistic to say that the Western Allies could get to Warsaw before the Soviets. Getting to Berlin first seems fairly likely, though. Perhaps Austria and the Czech Republic (sans Slovakia) would be mostly in the Western Sphere in this timeline. On the flip side, the Soviets would still no doubt move against Japan, perhaps almost a year early. This could result in a more rapid victory for communist China and a fully communist Korea. There might even be a communist Hokkaido, though this might be a difficult prospect for the Soviets if the Japanese determinedly oppose them.
Regarding Mediterranean operations, things could be highly varied. I'd have trouble seeing more than a few divisions in Africa moved to France. The rest would probably be sent on invasions as soon as enough ports were captured in France to permit dispersal of the amphibious force (perhaps even before for small landings like Sardinia/Corsica). The idea of Italy going neutral is interesting, but I'm not sure if either side would really make optimal moves here. At any rate, if there was an Italian campaign, it would be even more of a sideshow, and the Italians would certainly be even less motivated. A Greek campaign is also certainly possible at some point when the Germans decide to pull out. Getting further than North Macedonia and Bulgaria is probably not possible due to bad terrain and logistics, though, at least until the Ruhr is cut off and the Rich starts to crumble.
Regarding Kursk, it is interesting to consider the Germans quickly launching a successful early Citadel before reinforcing the west. The couple weeks delay would be more than made up for by the eased situation on the east front. However, even in this situation, I have a little bit of trouble seeing the Allies checked on the Seine for any length of time. The front is just too big and open. There would likely be a more harsh check of the Allies at the Siegfried line, though. However, I'm not convinced that the Germans wouldn't just cancel Citadel. They might make this move and prepare three panzer corps to be sent west, only to cancel the order for one of them when the Soviets launch powerful early attacks at Orel and Kharkov.
Regarding deception, this was something the Allies were particularly good at for invasions. I could easily see the original poster's scenario playing out with an identical German deployment in May 1943. Maybe a couple divisions would be moved around if the Germans caught wind of something, but I have trouble imagining the Germans actually being well-prepared for Roundup. They would no doubt transfer most (but not all) of their Italian mechanized forces and some miscellaneous infantry units, though, as soon as they heard about the landing. Probably not much from Norway, though, for the same reasons as historically. Neither these forces nor transfers from the east would likely arrive in time to contain the Allies like they were historically in Normandy until Cobra. In a worst case scenario for the Germans, these German forces get wrecked in a series of meeting engagements in France, as some historically did in 1944 (though I can see some of these going in favor of the Germans due to surprise, the Allied command of the air and far greater mechanization just gives them an overwhelming advantage in this situation).
I don't think the British would be in a much better place after a 1944 victory than 1945. Their losses would probably be similar due to the greater intensity of fighting and greater initial proportion of British troops, maybe a little less, and the extra year of peace would allow for a slightly faster recovery. Still, this isn't a fundementally different situation. I'd expect the postwar to be similar for them.
Overall, I think that this means the Allies get ashore easily and expand the bridgehead quickly, despite a weaker for than Overlord. Powerful German forces cause some setbacks around Paris and points east, but by this point, the Allies have ports, and new forces are pouring in rapidly. The front line stabilizes along the Siegfried line (a little further west than historically) and the Allies are slowed greatly at this point. They need time to recover from losses from battles with strong German reinforcements. Hitler will want to do some Bulge-like attack, which could be in winter or spring before the weather becomes good. It will fail, of course, since by this point, Allied logistics and forces are almost equal to the historical level a year later. It might get a little further, depending on how much the Germans denude the east front. When the weather is good, the Allies will launch a big attack. It was be much tougher than historically at first (a greater proportion of German reinforcements are now going to the west because of immediate danger), but they will probably breakout in summer 1944, with the war ending in fall at latest.