Re: toilet on peer and beam flooring
If you have determined that the subfloor is in sound condition, I would try re-setting the toilet, with a new wax ring, and use hard plastic shims to make sure the toilet is not hung up and rocking on an unevenness of the tile (the flange could have been set too high as well). Use a level across the rim to guide you to the right shimming locations. You may have to caulk around the base to hide the gap. Caulk only the front and sides, so a leak can be detected before reaching the catastrophic stage.
If the subfloor is unsound, you have quite a task ahead. But it starts with removing the toilet and taking up the floor. Since there is presumably a crawl space, you should be able to evaluate the subfloor from underneath, though.
Remove not the ancient landmark, which your fathers have set.