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The Ju 188 with DB603 engines and a bigger bomb bay could have filled your requirements. The designers need a genuine 2,000hp plus engine to play with but not a multi bank monster.
Schnell bomber = Fast Bomber.
The Jumo 222A powered Ju-288 had a max speed close to 400mph. Isn't that fast enough for you?
Hello GrauGeist
IMHO Ju 88G-6 was a better night fighter than He 219A-5, so why?
IIRC LW bomber crews liked more Ju 88S than Ju 188, so it seems that they prefer Schnell Bomber idea, so maybe Ju 188 without the upper turret and a MG 81 in place of MG 151 nose cannon or maybe the Mossie with DB 605 engines like the Finnish Vihuri design. The WWII era twin, not the post-war trainer.
Juha