Update: Problem solved
I'm glad to report that after installing two correct engine mount bolts and loosening everything up I think I've solved the problem. I loosened up the sides and bolted in the engine with new factory engine bolts. I then put everything on besides the belly pan on the bottom and everything seems to be working. It rolls when the rod is pushed down in the roll position, it starts up in neutral, goes in all gears, and reverse. Mowed the entire back yard with it. Retightened all the bolts after. Just need to address the loose steering, lube the chains with some chain lube and put the belly pan back on. Maybe install a fresh blade. Besides the original engine, it's practically a new mower. Engine fires up first try too. It cost about $70-$80 to rebuild the entire rear axle. It was $45 for the new friction disc and about $35 for the chains. I guess these mowers were never quiet because of the chain drive system. Only a little noticeable drop in noise level after a rebuild. I looked for one of these mowers for a long time but I heard most people threw them away so it was actually quite hard to find.