I want to go at this in a slightly different, but related way. I'm looking at getting a card that as a $120/year rebate for Avis rentals. However, it is not Primary coverage like my Sapphire. So, I'd want to book the car with the Sapphire for the coverage.
Then, assuming nothing happens to the car, I'd want to change to the other card upon return for actual payment. I'd only need to do this once a year for the rebate, so maybe the hassle is worth it once. Question is whether this would be allowed at return.
Cheers.