you can’t say that you have the gears aligned if you alxe moves 0.125 inches. I’d would not have my gears any more than 0.050″ out of alignment. Not having a view of your gears and chain, maybe replacing the chain and gears plus the bearings is called for. You have at least damaged the rear gear and maybe the drive gear. The chain also can strech and your’s maybe have been stretched to one side as well. Start by removing the play in the axle and see what happens. You may wind up replacing the gears and chain after that.