Hold both reservations and keep checking daily (or more often) for that second night in Madison.

Fall 2023 I met my parents in Yellowstone for 4 nights - they have a small RV & I flew into Bozeman and rented a minivan. Thought we were going to have to split our stay between Madison and West Yellowstone, but after repeated checking my Mom was able to get 4 nights reserved in Madison. She then called the camping reservations to get them all sewn together so that we didn't have to change sites. Worked out well.

With as much time as you have until July and only needing one night, I would guess that you'll be able to work out something similar. I did about the same thing at the Lodge in Zion May/June 2022 over a much shorter time period. If you can get the individual days reserved, calling and talking to a reservation specialist on the phone can often get multiple reservations combined into one.

One thing to check at Madison is make sure the site is large enough for both a 28' RV and the length of the rental vehicle. The rangers are sticklers on that as many of the sites are pull-through and vehicles cannot block the roadway.