Aside from posturing, the EV transition would end gas sales, thus ending this mechanism for funding roads. A per mile tax seems like a fair replacement.
Unfortunately common sense vanishes when everything is a chance to demonstrate which tribe you're a member of.
You could put a GPS tracker in the car but a lot of people won't go for that. Efforts to put more telematics in cars such as
https://en.wikipedia.org/wiki/Dedicated_short-range_communic...
have gone nowhere because nobody can find an agreeable solution for security, privacy, how to pay for the infrastructure, etc.
I like your GPS-based toll system idea. Different roads could have different toll rates that are displayed on your device, including a meter for how much you owe, and all jurisdictions can get their money. Fueled up in one state and drove through an intervening state en route to another? They can get their money. Heck, you can do it on a county level. You can fluctuate the toll rate to effect congestion pricing.
There's a lot you can do with this idea!