There were two levels of 'Mosquito fast', depending on engine line. Versions powered by the Merlin 20 and 30 series were good for 350-370 mph ('gunned', FB versions being a bit slower), and versions powered by the 2-stage Merlins (mostly bombers in ww2), going 400+ mph above 25000 ft. Achieving the 1st 'level'* should've been achievable came mid-1941, with DB 601E and BMW 801C coming online, especially if the number of guns sticking out is kept under control.Getting 'Mosquito fast' is tricky, though presumably they did it with the Arado 234. It just needed to arrive earlier, and maybe a bit more debugged. Could they do some equivalent earlier with piston engines? Not sure. Tomo's idea of FW 187 is fairly convincing. Fw 190G looks pretty good too for at least part of the problem.
Not quite 'Mosquito fast', but say, 'A-20 fast' plus some decent defensive guns seems also like a viable route to go. It would have been better than what they had with the Ju 88.
Achieving the 2nd level might've been perhaps achievable, even if at 20000 ft and not at 25000ft, with the fully rated BMW 801D, ie. from the late 1942 on? The resulting aircraft will need to be of modest proportions, talk half-way between the Fw 187 and Bf 110/Me-210? Or, have the Fw 187 being powered by the DB 605A?
FWIW, Focke Wulf was offering the fighter-bomber spin-off from the Fw 187 with either DB 605A (supposed to do ~650 km/h with a 1000 kg bomb, or 680-690 km/h clean) or BMW 801 engines, RLM was not interested.
* the early A-20s were supposed to be almost as fast, clocking 349 mph
From what I was able to gather, these worked well, and were scoring some kills.How good or bad were the remote defensive guns like on the Me 210 or 410? On the Grief? Did they work?