Moving and buying a car while temporarily without an address

My husband and I are going to be moving from Illinois to Vermont, and between selling our house in IL and moving into our new house in VT we will be staying with a family member for a few months and building out a camper van.

We need to buy the cargo van and would prefer to do so after we leave IL partially because we don’t have a great place to park it at our city home, and partly because we don’t want to pay the high registration fees for Chicago when we’re just going to be leaving.

But if we buy it after we’ve left, we technically won’t have an address. Plus we’ll be staying in a state different from our drivers licenses.

We are going to be purchasing the VT house before we leave here and renting it back to the current owners until we move in, so in theory we could go to VT and get our licenses and then buy the van and register it there, except we won’t yet have any of the address verification documents like utility bills in our name, so not sure that’s possible either.

This whole thing is really breaking my brain - does anyone see a way to get through it that I am missing?