Another interesting potential option is to put the extra resources into Me109s, four per He177 in terms of engines and material weight. IIRC that would be at least 500 extra fighters over the course of 1942 plus spare parts, which would be a huge help in the Mediterranean, as there some 900 fighters were lost in late 1942-May 1943 in Tunisia, which then left a big deficit to defend Sicily. Having those extra fighters in 1942 and in early 1943 (several hundred extra more) then Sicily could actually be defended from the air. IOTL the Italians and Germans each lost over 2000 aircraft in Tunisia during that campaign so the addition probably 1000 fighters that would be built over the time frame could mostly appear there to make up for the deficit. Based on my read of Murray's Strategy for Defeat the equipment losses in the Mediterranean were very severe during Tunisian amounting to 41% of the Luftwaffe equipment totals in November 1942 (but clearly spread out from November 1942-May 1943) leaving many pilots without mounts, both Italian and German. What aircraft were left often lacked spare parts due to the loss of stocks in Tunisia, so were unable to keep up with the sorties generated by the Wallies.
So with the extra SE fighter production as a result of no He-177s then there would be sufficient spares coming out of factories in Germany and replacement fighters for German and Italian pilots. Assuming all the new fighters went to the Mediterranean than that would replace all the fighter losses the Germans have suffered and probably provide a surplus that could be used for Italian pilots. That could have a huge impact on the ability of the Axis to defend Sicily even with the major ground unit deficit that existed after Tunisia. If able to blunt the Wallied air offensive during the May-July 1943 period then the Axis forces had an actual shot of defeating the invasion; IOTL the Axis offensive air units were put out of commission due to the bombing campaign on Sicily, which was successful due to the Axis fighter strength being mostly wiped out in Tunisia when the airfields were overrun. Having hundreds of extra fighters and sufficient spare parts to keep all of the aircraft generating sufficient sorties then means the fighter-bombers and naval bombers could actually get off the ground to attack the densely packed Allied naval armada and potentially remove the trump card of naval bombardment of Axis ground units counterattacking the beachheads that ensured the landings were able to get a foothold.
If Sicily doesn't work and the Mediterranean Allied air force gets much more bloodied, then that changes the strategic situation in Europe quite a bit for the rest of 1943 and into 1944, not least because the inability of the Allies to put convoys through the Mediterranean, but also the likely political fall out and reserve that allows Germany for 1944 in Western Europe, plus the Italians remaining in the war on Germany's side.