Hello again,
As mentioned earlier I think that the 2:1 geared shaft is a rotary valve used to time the intake into the crankcase of this engine. I also still think this engine is pure 2 stroke - not a combination of 2 and 4 stroke. Let me try and explain my reasoning again (perhaps my last attempt was poor)...
If the rotary valve were to be a piece of bar that is cross-drilled, then the periphery of the bar will have 2 openings on it that are set 180 degrees apart. The fact that it would have 2 openings that are set 180 degrees apart, is the reason why the 2:1 gearing would be needed. If you look at any model engine that uses a rotary valve in the front of the crankshaft, you'll notice that it has only one opening on the periphery of the shaft and that it also (quite obviously) rotates at crankshaft speed. The best direct comparison that I can think of at the moment would be to put two holes/ports into the disk valve on a 2 stroke engine that uses a disk valve. If these 2 ports were to be 180 degrees apart, then the disk valve would have to rotate at half crankshaft speed.
As for the rich/lean problem on a pair of cylinders in the 'vee', would it not be possible to adjust the transfer ports so that they are biased towards a cylinder?
I hope this makes more sense than my last attempt.
Regards
Warren