We had something similar to this happen with Alamo. We were about 20 mins early and asked if we could pick up early. We were told since we got a low rate with a coupon, we would have to pay the difference. Thinking 20 mins wouldn't matter much, I asked the cost. It was originally around $75 and the price was going to go up $50!!! We waited till it was time for our original reservation as we were not about to pay almost double for 20 mins! And they also made us wait to the minute (actually, a few past) before they would process us.
YIKES!!!!

That's what I don't want to have happen.
Think I'll just reserve from 9:30 and pay the few extra dollars per car, rather than chancing it and getting stuck waiting or paying the exorbitant extra fee!
Thanks for sharing your experience!