I have a Maine Coon as well.
She has become deathly afraid of the vet's (drooling constantly when there etc) so I'm doing all I can to make sure she doesn't associate the carrier with the vets, which means keeping it out all the time. Fortunately, she loves to sleep and play in it, so hasn't associated it with bad things so far anyway.
In addition to all the other suggestions, I would suggest you start feeding your cat in the carrier, that would definitely make him more comfortable with it. Perhaps slowly move his food bowl first closer to the carrier, then next to it, then to the door of the carrier etc. Once he's used to being in the carrier, try closing the door. When he's used to that, pick up the carrier and walk around with it, then go for a drive etc and even once he's used to it, keep taking him for a drive or something in it on occasion just so he doesn't associate longer trips in the carrier with the vet's only. This way he'd become used to traveling in the carrier, but of course you have to make sure you go so slowly the cat doesn't become scared at any point, I'm sure you know what I'm talking about. Just think of it this way- it may take you weeks or months of work to get him used to it, but once you do, it's going to make his and your life a lot easier and less stressful from then on.
I wouldn't recommend the harness until your cat's very used to it and you find one that's tight enough (but comfortable for the cat of course). I know that when my cats freak, they manage to get out of their harnesses in a flash, no matter how secure I thought they were, I just don't understand how they can twist and turn to get out of the harness, but they can. Well, the Maine Coon doesn't freak so she hasn't done this yet, but my other cat has so I'd be careful with the harness idea.
Oh yeah, almost forgot... The panting is probably a sign of stress. Cats can pant because they've been stressed out about something (in this case the scare of the vet/carrier) and it can continue for a while after the situation. Nothing to worry about as such, just a sign of the overall anxiety he has of the situation. Btw, my Maine Coon even pants when she's been playing VERY hard.