Yeah, I'm not understanding why finishing the basement isn't the ideal option, even if you end up selling, wouldn't that Reno add a ton of value?
How far are you from FIRE?
I personally don't believe in "forever homes", but absolutely understand buying a long term home for your remaining working years. After that though, who knows what you will need and want from a home.
So if retirement is years away, you've got quite stable careers, and as long as you work, you will have the same predictable needs from a house that this one can't provide, then moving might make a lot of sense.
If you're just a few years from retirement, and the teaching in the cold basement thing is your biggest issue, then I would lean towards just solving that issue and waiting until retirement to sell.
Out of curiosity, what's wrong with the rest of the house that it needs a full gut job? You said that all of the previous owners have invested in the house.