I've run into this with airlines and rental car companies: being polite and asking if there's anything they can do to help some situation be less cruddy (even it is
was your fault that you missed boarding your flight) often nets something that's at least passingly-pleasant
Had Hertz (my least-favorite rental company) give me a discount on a substitute vehicle because I really didn't want to be driving a Suburban for the week (I'd rented a midsize, but they were out of everything but full-size SUVs). They knocked it down to a compact rate for the week (which, to an extent, I didn't really care about - it was a work trip, but I also didn't need all the space and hassle of the big vehicle)
Delta gave my wife and I $400 travel vouchers, rebooked us First Class home, and gave us meal vouchers to make up for getting our honeymoon return trip broken (somehow we ended up on different itineraries). This was right after watching the counter rep do the absolute least to the family in front of us that was extremely rude to the rep.
Just SMILING at the counter rep can make a world of difference :)
I used to get free upgrades at Dollar next to Bradley airport just because I smiled to the manager and his fiancee-then-wife when I'd come in and ask how their weekend was (I spent ~8mos flying into BDL every week several years ago - all but about 3 of those trips utilized Dollar for my car rentals): I'd book the compact of "manager special" rate, and always got bumped up a class (or 4) ...just for being polite