Hi
Ok, so I'm not a dog expert, but have a bit of experience in people health
I think a video-fluoroscopy sounds like a good idea (basically give a food with x-ray contrast in it), this assesses the physiological swallowing of your dog. It may be very useful to delineate the swallowing issue. (This is done on humans a lot)
Sounds like your pup has been on a lot of antibiotics aswell. It may be good to evaluate how the periods off the antibiotics were in terms of health. (Do you also try natural yoghurt to try and balance natural flora.) It appears that many people on here have suggested some of the "conditions" the antibiotics were prescribed for are fairly normal puppy issues.
It definitely is worth considering seeing a specialist vet if this is what is offered, or getting a 3rd opinion. Remember the vet you see has to be very familiar with many different animals, and it is possible that your pup has an uncommon condition that is best managed by a specialist..
As for sending pup back, I'm no help there. Its a very personal decision IMO.
Good luck