If you go the relining route, there is your answer. ^^^^
Honestly, though, I don't see any point in spending money on the old gun. The few that go for the prices mentioned are ones in near new condition, not ones rebarreled and rebuilt. IIRC, those guns were reproduced a few years ago and those turn up fairly often in like new condition. Or just buy a good .22 bolt action and hang the old Stevens on the wall in honorable retirement.
Jim