How much of that patch of pitting below 'SAFE' actually shows with the safety button in place and in the 'safe' position. It might be covered.
Or in the least what little shows can be filed & polished out.
Perhaps the remaining areas on the top tang can be filed out and recut w/o welding too.
If you do weld around the gold inlay,,remove the gold first so it doesn't melt and flow into the weld.

They're beautiful, quality shotgun(s), I think they deserve the work to put them right.

If they're going for re-sale, those pits will be a tire kickers delight especially if other work shows on the guns.
Restore them IHMO. Then you'll never have to make an excuse for the pitting when showing them.