Welding the crankshafts isn't going to work for some reasons not menioned here. Basically, the top side of the bottom motor is covered by a combination flywheel and fan, and will not lend easily to welding anything together. This part is typically aluminum, or aluminum and plastic. You would have to weld from the bottom of the top engine's crankshaft to the very top surface on the bottom engine's crankshaft. This is a small fragile weld bead for what you want to do. Take into account the alignment issues as mentioned before, the weld won't last long.
To get this to work you could make an adapter which puts a coupler between the top and bottom engines. The adapter would be a plate the bolts to the top of the bottom engine's flywheel, using the nut which retains the flywheel to the crankshaft. You would have to key this adapter to the crankshaft somehow. Alternatively, some Kohler engines have drive systems incorporated into thier flywheels which use either three or four bolts. If you have one of these engines you could just bolt the adapter right to those threaded holes. The adapter would mount a couple, which is welded to a standard keyed sleeve going to the top engine's crankshaft. This would allow misalignment of the two crankshafts without shafing the whole assembly to pieces.
The timing issue really isn't an issue so long as you orient the adapter between the two engines, so that the little engine fires while the bigger engine is just beginning it's exhaust stroke (exhaust valve open). Doing this you won't have to worry about overspeeding the small engine, and you won't have to worry about the small engine's compression stroke bogging down the big engine's intake stroke. Speeding up or slowing down the intake stroke of either engine is going to hurt cylinder filling and reduce power of either engine. This is not the goal, however, it's unavoidable given that the two engines are so different in power levels. Orienting the big engine's power stroke to the little engine's compression stroke is as follows:
C) BIG SMALL
1) pow com
2) exh pow
3) int exh
4) com int
Cycle 1, has the big engine firing when the small engine is under it's compression stroke. I would orient the engines so that the big engine fires just after the small engine's intake valve closes. This will be some angle not divisible by a 90 deg increment.
Cycle 2, the big engine goes into exhaust and the small engine goes through it's power cycle. I don't see this process as hurting the big engine, since the big engine has alot more inertia and drag than the small engine. This is a better compromise than the reverse, where the little engine is on it's exhaust cycle and the big engine fires. You will overspeed the small engine for sure in this scenario.
Cycle 3, both engines freehweel, no difference from the factory setups.
Cycle 4, big engine goes into it's compression stroke and the small engine goes into it's intake stroke. Cylinder filling on the small engine will be effected less by the big engine's compression stroke than it would be if the big engine were on it's exhaust stroke. The exhaust stroke of the big engine would offer less resistance to rotation causing the small engine's piston would move faster, not necessarily making more power in the small engine.
Now, if the engines were ganged to fire 180 degrees apart, then the small engine's intake stroke would occur on the big engine's exhaust stroke. this again would cause much higher piston speeds than normal in the small engine during the intake stroke, and less cylinder filling.
Ideally, if both engines are the same power level, then run the firing events at 180 degrees from each other.
I see no reason to try and balance the carbs, since the following two things are true (as far as I can tell).
1) The two engines are completely different power levels.
2) Balancing the carbs would bring this whole project to 98% half-assedness, rather than the full 100% half-assedness, using unbalanced carbs. I don't see the time invested in balancing the carbs as worthwhile given the meager 2% reduction in half-assedness. Granted, this is also a good argument for just welding the cranks together instead of building an adapter/coupler mechanism. This is how I see it, please take no offense.
