If you're running the transmission horizontal, then that could be a problem because as mentioned- the grease is going to leak out. I suppose there's two ways to look at it. First of all, with those large bicycle wheels I imagine that the transmission isn't going to be turning very fast to get to any sort of speed. I am using a racing mower with tiny 6" wheels ( 9 " with tires) and using no transmissions- just a right angle gear box. That gives me a speed of around 35 MPH max. You're using huge 26" wheels thus about a third as much output speed is needed.
I think it might help simplify your build if you reconsidered your engine and went with a vertical shaft instead- say like a conventional 4-5 HP push mower engine. That way you could utilize the transmission as it was designed. The output of the engine would be aligned with input of the transmission and the output of the transmission would give you a straight chain drive to the axle. If you look at most of the builds here, it shows you how that setup works. Might give you some ideas.
Anyway, I'm no engineer but maybe that helps you a bit.