Those arches are well and truley salvagable.
it looks like the rust has crept in from the edge under the paint, rather than come through from behind. So i don't think there is any extra hidden rust, which is often a problem with arches.
So i reckon, grind out the rust, use a sanding disc or belt sander rather than a wire brush. wire brushes sometimes just polish the rust rather than remove it all.
use a rust treatment on any remaining nooks and crannies.
weld in a bit where it has rusted through.
after it has painted i would use an anti rust wax treatment, like dinitrol or something similar (not waxoyl, that's rubbish). spray it on the edge of the arch where the water got in before.
you said it had a plastic cover over the arch, so that should hide where the wax is.
This won't last forever, but then neither will new arches