Calling the location has proved useless every time I’ve tried and with different locations — particularly an airport location. When I’ve taken it up with staff they always say they are just too busy to answer. It certainly seems true.
When I’m doing what the poster wants to do, I’ve stopped using the rental car return lane, particularly when the airport is crazy busy. They tend to get irritated with cars blocking the lane (don’t blame them). I park very nearby. Some depots have other parking you can use to go in for a re-write or similar.
Not sure of the poster’s situation but there are times when having a new/separate contract is critical. For example, my CC insurance could be jeopardized if there are back to back rentals. Solution, just use a different card for one of the rentals. Of course, every person’s situation and coverage is different.
If the second reservation is on reward days, the poster can likely call in to the EC line and get them to do the paperwork, apply the free days, and email a revised contract.