FWIW, besides some 147 of the B series engines, the Paterson plant was making only the A series (some 23000+ engines made between 1938 and November of 1944 - end of production? November saw just 4 engines made). The B and BB series were made in Cincinnati, at the notorious Lockland plant; some 43000 of R-2600s were produced there, the 1st R-2600 was made in June of 1941.
Patterson was the 'home' of Wright aero engines of interest.
Whatever the 2-stage S/Cs took wrt. the indicated HP, they gave a good part of it back via the incresed exhaust thrust at the higher altitudes (exactly where the S/C was requiring the greatest power to do it's job), as well as by enabling the aircraft to fly in the less dense air for the max speed.
Granted, if the exhausts are badly designed, as in the case of the F4F, a lot of that exhaust thrust will be lost beforehand.
One of the ways to improve the R-2600, without going with the additional stage of compresson (be that by turbo or by a gear-drien aux S/C) might've been the installation of a bigger engines-stage S/C. With just an 11 in impeller, in the higher altitudes the R-2600 will never be as good as the Hercules or BMW 801 with their 13 in impellers* (and even these needed upgrades to further improve the altitude power), or the Kasei 20 series.
Yes, some power down will be lost, but for a fighter that takes second place behind the altitude power.
Better cooling was feasible via the installation of the cooling fan, or via the 'explosive' cooling like the Lewis gun had, where the exhaust gases are increasing the speed of the cooling air drawing it backwards.
*some post war Hercules versions were also available with 14 in impellers, while some low-altitude ww2 versions were with 12 in impeller