To flip the things around - what might be the best way for the BMW to much improve the fortunes of the 801?
(hopefully the OP will forgive me here

)
There was 80 of 801E engines made, but that version didn't make in production (engine have had, among other things, a much improved S/C, thus the engine power at 5.7 km was same as with 801D at km, ie. in low gear). Seems like both BMW and RLM were of opinion that it will take some time to modify the tooling for the 801E to be made in existing factories, so the 801E never went into series production.
(question is then - how much time they were expecting for the 802, let alone for the 803 to materialize....)
So press on with the 801E by winter of 1942/43, so the equivalent of performance of the 190D-9 can be had almost two years earlier with lighter and more streamlined A-3 to A-6 basic airframes.
A 2-stage supercharged 801 would've also been a sight to see, ie. something like the BMW P.8028.
A 3-speed drive for the 801E, with 3dr gear clutched in above 7 km?
(eventually the 801E's supercharger and plumbing for it were shoehorned on the 801D to make the 801S, but that was too late)
Copy the Sydlovsky-Planiol control mechanism for the S/C for a really smooth power curve?
Introduction of MW50 system?
Greater proliferation of GM1 for the Fw 190s?
Better fresh air intake is a must, but much better streamlined than
it was the case historically.