Got a diagnosis; the gas is leaking from around the place where the fuel filler neck connects to the tank. The guy working on it doesn't really want to do welding on the gas tank (I can't imagine why, heh heh), so I'll be calling used auto parts places tomorrow to see what they're asking for a used tank.
Bringing the car to the mechanic guy gave me an excuse to be near Missoula, so I also picked up some tools of the trade.
The black foam is pipe insulation. It's a bit more than 1.25" for the outside diameter, and it's already split down the side. It's hollow on the inside but the open area is small enough, and the foam is thick enough, and it's already an arch shape, that I think it will be able to resist being pushed in by the modest air pressure at the front. It has adhesive down the sides of the split, but it's easy enough to pull off so I can replace it with something like Goop.
I also got Gorilla Tape for making turbulators for the A-pillars and top of the windshield (and maybe other places too), and it will be useful as tape too I imagine. And I also got some clear caulk so I can seal some areas on Car without it looking like I caulked them.
I hope I find a tank for not too much money.