Update on this: I replaced both 3 way switches and when energized they work properly. Tested old SW1 and SW2 with an ohmmeter and SW1 did not ring out at all, which is strange. SW2 was fine. Both were wired correctly.
With the old switches still in place, I used a solonoid tester and it was a weak LED signal around the 12 volt range with both switches in the off position.
With the new switches in the off position, I'm still getting the same signal. So I think a different circuit is sharing this neutral somewhere. I'm going to try and trace it and see if there's a shared JB in the basement. If I can't find it, I'm just going to leave it as a switched neutral for now. I was planning on rewiring it anyway, but not for awhile.
Hell, it's been like this for over 50 years - another few months can wait.