All of this is probably not far off the mark.
The SK leadership - if successful - will quickly figure out that their conceptions of Allied policy flexibility were sorely mistaken. At that point, their options become far less pleasant. Especially once they learn of the full scale of the Shoah.
What can they do about that? Shut down all mass murder operations, of course. But also, perhaps, a cover-up. Eliminate the last few survivors in the death camps (the sonderkommando) as potential witnesses. (This can be rationalized on the grounds that they assisted in the murders.) Bulldoze the sites; send the Totenkopf-Verband to die in battle on the Eastern Front, and destroy every scrap of documentation. It won't really work; many of the worst crimes were committed at the concentration camps in Germany, where there were lots of survivors, and Auschwitz was a hybrid site. But they might try it, fearing that the Allied reaction to the whole truth will be to abolish Germany culturally and even biologically. (There were proposals OTL for Germany to be placed under permanent quarantine and population controls.)
1. Re: Allied-Soviet relations and suspicions : One thing to remember as well is that the final occupation zones were not decided until the London Protocol beginning in September 1944. Now those discussions are going to be taking place in the context of an SK-led Germany trying to find a way out of the war, and which has already withdrawn from France and most of Belgium. It's increasingly obvious that the Germans have redirected most of their efforts to the Eastern Front. Churchill, realizing that the Allied armies are now likely to end up farther east, will be pressing to minimize the Soviet occupation zone (along with his pet Adriatic landing operation). Soviet suspicions of the Western leaders will now be pegging the meter. Stalin may even break off the discussions and have his delegation leave in a huff.
Will Stalin go that far? Britain and the U.S. will bend over backwards to placate his suspicions, and he has high-level agents in both governments to confirm that there are no secret dealings with Germany. If he does, maybe Churchill and FDR blow him off; if they can't satisfy him at all, there's no point in trying - so why not talk to the SK?
Probably not, and they would have to act quickly - the Warsaw Uprising was only 10 days after VALKYRIE.2. This raises in turn the interesting question you raise here of how the SK government (however led) would deal with the Home Army uprising. It is hard to play that out. The smart move on the part of the new government would be to cut a deal with the Home Army and leave them in control of most of Warsaw and perhaps even other pockets, on the theory that an intact, armed Polish Home Army controlling some key territory is going to heavily complicate Soviet occupation efforts in Poland, and possibly even its supply lines as it moves west of the Vistula. It will also ratchet up Stalin's paranoia that Berlin has been cutting deals with London and Washington (whose solicitude for Poland's political future is already well flagged and intensely irritating). But would they be smart?
There's also the problem that if the Home Army overtly accepts anything from the Germans, Stalin will cite it as proof they are just fascist bandits. Unless the Germans withdraw from the whole area, he will accuse the Poles of collusion. OTL, the Germans counterattacked east of Warsaw, and pushed back the Soviet spearheads. If they still do that, but don't reconquer Warsaw, it looks... odd.
3. In terms of territory, one suspects that, in broad strokes, the Western armies will indeed end up a little farther east.
Maybe yes, maybe no. If the Germans get out of western France immediately, they can probably contain the COBRA breakout further west, and hold Antwerp long enough to wreck the harbor thoroughly. Also, if the Germans decide to get out of western (and therefore southern) France right after COBRA, then they will know two weeks ahead of DRAGOON that they are leaving southern France, which is a lot of time to wreck Marseilles and the railroads to the north. So in late summer and fall 1944, the Allies in France will be facing more Germans, with less supplies. The Allies can bring in additional troops from Italy, which will go quiet at the Alps, but the supply difficulties can't be fixed till the ports are repaired, which will take months. (OTOH, if the Germans evacuate Brest and the Gironde estuary, and the Channel ports, those become available.)
The Soviets will face additional difficulties too (e.g. 20 divisions from Courland to the main front) but also advantages, especially in the Balkans, where the collapse of the Axis will be faster and harder.
And there is still the big question: does Germany fight to the end? OT1H, surrender is a very bitter pill, and no one wants to be called "traitor" or "backstabber". OTOH, by this time, it's getting pretty obvious to almost everyone in Germany that there is no chance to win the war, or even avoid defeat, and that every additional day of war means more German cities bombed and more German soldiers killed. The SK have some conscience, and a lot more concern for the German people than Hitler ever did.
But who's going to bite the bullet, and say the Emperor has no clothes? And how will the German people react to the events after VALKYRIE, especially the absence of Goebbel's propaganda? If German morale breaks in general, there could be a sentiment parallel to the support for Vichy France, i.e. "We've lost, now let's stop getting shot at." Italians in 1943 generally welcomed the surrender and Allied occupation, as they were thoroughly sick of war.
When? Bear in mind that Lend-Lease aid to the USSR is close to peak in 1944, with the Soviet forces heavily dependent on L-L aviation fuel, trucks, explosives, and a host of other stuff. If Stalin blows his fuses and goes rogue, the U.S. stops Lend-Lease.4. It's quite possible now that Allied-Soviet relations essentially dissolve in mutual acrimony.
The Balkans could end up in a messier state, too. OTOH, Allied forces might end up making more progress in NW Yugoslavia and the Dalmatian coast, leading Tito to strike out for a more independent line of Moscow more quickly. On the other hand, there might be no "percentages" agreement between Churchill and Stalin restraining the latter from giving active aid to the Greek Communists.
Churchill will want to move east from Italy; if the Germans bail out of Greece and Albania and southern Yugoslavia, that is an opportunity. Also recall what I suggested about Bulgaria. Unfortunately, the Soviets got to Bulgaria by about 1 September, OTL. That doesn't allow much time for the Germans to decide to get out of Greece, and for the British to move in and then through to Bulgaria (which is all the way north - much harder than just landing in Athens). The British reached Athens in mid-October OTL. That could move up a month. Another point: OTL, there were German hold-outs in the islands (in Crete, for instance) till V-E Day. (I've seen squib references, have no details.) I'd guess they were caught there, unable to evacuate, like the Germans in the Channel Islands. If the SK move faster on evacuation, can they get out? If not, with Hitler gone and Germans retreating everywhere, do those garrisons just surrender? OTL, when did the Allies actually liberate or occupy the various Aegean islands?