Derp. Week later update. Cell coverage was almost non-existent out there and even in Cody the internet was shit.
Eagle managed to find me and get me two tires on Monday. They had to order them from a supplier and I didn't get the car back until 5 Monday afternoon. They did manage to find a pair that were almost identical to the originals.
The fun part is, I apparently left the cargo "floor" of the rental on the side of the road when I put the spare on. When I got it back from Eagle, I noticed it was missing. I called them just to check and they confirmed it wasn't there when they go it. (I vaguely remember showing the driver the other blown tire in the back and realize it wasn't there at that point.) I ran back out to the scene of the crime early Tuesday on my way back to Billings, expecting to find it out there. (It was very remote.) Unfortunately, I noticed a bunch of side by side tracks on the way out and I'm guessing someone found it and picked it up as trash....to which I'll give them credit - the trails out there are SPOTLESS.
So I returned it, sans floor. Still haven't heard a peep out of the rental company. 🤣
The good news is, I put this on my "good" credit card that has great coverage for travel. It has primary rental car coverage (unlike most that are secondary that make you put it on your auto insurance first and only cover what's left) so I'll be able to open a claim and get it paid for. Ended up being like $830 - over $500 for the tow and $260+ for the tires plus taxes and other fees. Fuck me.