I was told at the counter when I got the car that there was no 29-minute grace period. I found that surprising, but I played it safe, and I kept a target time of 3:01pm, based on our exchange above.
I’m glad to report a happy ending of my rental adventure. I returned the car a bit after 2pm and there was no additional charge.
In fact, a few hours before returning the car, United canceled my flight due to the intense storms on the east of the US. I had to drive 2 hours and return the car at a different airport. Believe it or not, I got no drop-off charge either.
I still intend to write to Hertz customer support to complain about the 2-hour delay.