If you could turn the mower gearbox 180 degrees so the input shaft faced the front of the tractor, you could have a straight driveshaft and 2 sets of pulleys. Or maybe drive off the crankshaft somehow.

Is there anyway to get your drive off the belt pulley on the tractor instead of the PTO?

I wondered, too, how the mower was driven before. As far as I know, all tractor PTO's turn the same direction.

Just throwing a bunch of poo against the wall, maybe something will stick.