this should give those who claim it wasn't possible some food for thought
out of correctness for the above author: his name is properly spelled Dietmar Hermann not ............... harmann
The problem isn't so much the firing rate of the gun, which is actually controlled in a synchronized gun by the synchro mechanism, but by the variation in timing between primer initiation and projectile leaving the barrel.
A variation of 1/100 of a second isn't going to mean much to the cycle rate of the gun or even that much to the muzzle velocity of the projectile but it can mean a great deal to the position of the propeller blade.
Why not design the Fw-190D9 specifically for the Mk103 3cm cannon?
The P39 engine was mounted behind the pilot. You could do something similiar with the Fw-190D9. Mount the heavy cannon and ammunition in the rear to balance the front mounted engine. The cannon barrel would be in a tube which runs under the pilot seat.