OK, here’s the latest. I’ve flown three times in the past month with a Blevins Marie 24, slightly bigger than a Harpsicle. (Dimensions, from Blevins’s site: 36″ h x 8.5″ (soundboard width) x 19.5″ (front to back))
Absolutely no problems, even on the flight that was completely full. The flight attendants kept an eye out and made sure nobody crammed their suitcases in with the harp.
I am lucky to fly on the A list, and so I was always one of the first 30 people on the flight. I doubt that you’d have a problem unless you ended up with a B or C boarding pass, so I think it would be worth your while to pay the extra $10 each way for the earlybird checkin.
Good luck, but unless you have a last minute delay, I think you will be fine!