What's important is to get the shorted wires separated if only by a thousandth or two.
If they didnt spot weld together you can probably fix it. If you can pry apart any spotwelds you can fix it. What's deadly is one you can't reach.
My dishasher motor did same thing last summer. The entire start winding turned black.
The fault where the wires had spot-welded was visible, thank goodness for it's a $220 motor !
I poked the wires apart with an orange-stick from wife's manicure kit then soldered one back together where it had burnt in two.
Next I saturatated the windings with polyurethane varnish because it's nice and thin and will run down into the crevices between conductors. I massaged the windings to encourage wires to separate. After varnish dried i re-laced the winding with nylon twine..
Still running quiet and smooth , no more burnt motor smell. (knock wood)
I've never thinned JB weld. For your application it sounds like overkill .
I'd say use plenty of paint or varnish..
The electromagnetic forces act on the conductors themselves so you want both mechanical support against faint vibrations and electrical insulation.
How important is it that the insulation be the same resistance value as it is factory?
Not very. Dont worry about resistance of varnish at this low voltage.
To put it in practical terms, all you need is
'quite a bit'...