Safety **** reporting in here.
I wouldn't be very comfortable using that soft copper, Drew. It'll for sure deform and let the nuts come loose. I like your idea of double nutting. On my trailer, I welded a couple long bolts to the top rail, and used nyloc nuts to secure the spare. Been that way for fifteen some years with no issues, other than probably needing new tires because they're so old. If you're inconvenienced by all the extra thread sticking out, cut it off with a hacksaw and use your bench grinder to cut a taper on the ends so the nuts will start again. That way you won't need those copper spacers at all.
$0.02, and probably not worth that...