The problem sounds more like lean mixture than anything else (though it could also perhaps be poor compression, due to ring/bore/decompressor problems). Lean mixture can be caused in four main ways: intake pipe air leak; crankcase air leak; blockage in fuel tank/fuel pipe/fuel tap; or carburetor malfunction.
Because your carburetor works well on another mower, it is probably the least likely source of trouble in this case. Since the problem is worst when starting, the single most likely cause seems to be an air leak into the intake pipe or crankcase. Mowernut's specific suggestions are well worth following up, especially since you have some signs of a crankshaft seal leak. That kind of leak matches your symptoms (running better at high speed than low speed, and variable leakage rate) better than any alternative explanation. If the seal is leaking, it needs to be fixed.
