Rotten Floor under immovable claw tub

You need an engineer and an inspector to tell you what to do in this situation.

Sounds like your concrete slab is un-insulated around the perimeter and/or the bottom. The very conductive flooring material (tile) doesn't help; the combination of these two means that the floor has very little thermal resistance to heat flow, so you constantly lose heat through the slab.

If the heat you generate is quickly rising through the second floor, it sounds like you have a secondary problem of too little attic insulation, which is causing the rising heat to rise right through the attic rather than get stuck at the second floor ceiling due to all the insulation that should be there.

The second problem is easy to fix: go up into the attic and air-seal all the places on the attic floor that are open to the living space using caulk and canned spray foam, and then blow 15" or more of cellulose onto the floor, covering up any existing insulation up there.

The problem with the slab is harder to fix. If you have bare dirt around your house rather than a concrete walkway, you can dig a trench around it to expose the perimeter and add rigid EPS or XPS foam insulation panels (not polyiso, it absorbs water). If you do this, take the time to add perimeter drains too; there'll never be a better time.

If that's not an option, and I assume you'd like to keep the tile flooring, you can always cover it up with rugs. It's surprisingly effective. Russians love their rugs.

Finally, it sounds like you have a poorly-designed heating system. Even in a badly-insulated house, heat isn't supposed to pool in the second floor like that. Old houses with ducted furnaces but lacking much insulation commonly had all the returns on the first floor to encourage air mixing. But without more details about your heating system, it's hard to say more.