First, I think it is a great idea to seek a second opinion (even a 3rd if necessary). My daughter's pediatrician was so reassuring that everything was "fine". She did NOT have your son's problem... but she wasn't "fine", either.
As for hiccups... I wish they would tell us more about them. My daughter had them a LOT before she was even born, and they persisted afterwards. They slowly tapered over the decades. She is now 20, and she still gets them perhaps a little more often than other people, but not too much. They were a nuisance because in her case, they kept waking her up as a baby, and she was already a very poor sleeper (or who knows-maybe she was a poor sleeper in part because of the frequent hiccups.
Anyway, the doctors say they are "benign". That may not be our point of view, but medically... that's what we are told.
I wonder though.... are they connected to some (benign) glitch in the nervous system that they may slowly grow out of as their nervous system matures?
Sorry I have no concrete answers... just sharing with you...
-J.