For starters the term "Air Superiority" and "Air Supremacy" when used by authors of books on WW2 history, is interchangeable. What some post war USAF manual says is quite off topic, so you guys can end that arguement. English as a language is no that rigid.
Cherry picking one air campaign from 1944 as the "real end" to the LW is a flawed concept imho, there were too many pressures on the LW from many sources to pick one as the main cause. If I had to pick a "LW cannot win" date, I would pick December 1943, after that they were not going to have the #s of pilots and a/c to effectively repel a bombing offensive, or an invasion of France.
The LW continued to have impressive # of ac "on the roster"....but that was not the same as operational examples. My #s:
Luftlotte Reich as of June 1st 1944: 788 single engined day fighters of which 472 were operational. 203 twin engined day fighters of which 83 were operational. 991 day fighters of which 555 were ready for action. They continued to get deliveries of new ac in quantity, no doubt, but the bases, air crews, supplies and other infrastructure to sustain them was the problem.
Ah the Spitfire. Yes indeed. Its essentially a Spitfire F. IX with a merlin 61, and its #s match as close as other AH fighters. It has an upgraded E wing which was available either new or as a modification in 1944.