It might be easier to get a new alloy pulley that is a tighter fit.
That, or as oldiebutgoodie says, steel or brass shimstock, and then a drive fit (heat pulley, ensure inner end of hole has a slight chamfer).
OR... A good lathe turner could bore out the existing pulley and make a tight int. fit bush in fairly short order, again, shrink it in.
I think I would also try to get a better fitting key made, or sourced, but from good key-stock or at least 3/4 hard steel plate
I would also definitely use Loctite Bearing fit, once the tolerance is down below about 10 thou, it starts to work like a weld anyway
I would not weld it initially, the mechanical option gives you that final method if it does then fail. The motor components look very close to the weld area. (If you do weld, use Cold Front packed a round the shaft below it)
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Methinks the present (damaged) retaining screw thread one size too small!