I'd certainly not pay the bill in full. I've dealt with similar situations a bunch of times through my office and while no two deals are the same, here's a couple thoughts.
While its true you owe for time fixing the boat, that's on the assumption that he knows what he's doing, and it seems as if that' s not so much the case. Contracts go both ways;you agree to pay him for parts and service, but he agrees to use the right parts and do the correct service. He apparently didn't live up to his end of the bargain. I'd offer him a compromise amount, no more than half since he didn't get the job done. As far as the parts, I'd argue on that. Of course you owe for parts necessary to fix a problem. But if he just starts swapping parts and doesn't get it fixed, I'd tell him he can have his parts back, just return yours. He won't do that, so I'd again suggest a a compromise. Of course the exception would be if he said something like "I'm not sure its the carb, but I can change it and see, what do you think?" If you agreed to that, then you own it.
I disagree with the folks who say just bite the bullet and pay the bill. I'd dispute the bill, but pay something. If you don't give him anything, you're guaranteed a collection. If you at least give him something, you've got a chance he may not want to go to court.
One thing I'd try if you send him some money is to put a restrictive endorsement or "payment in full" notation on the check. You can write on the memo line something like "negotiation acknowledges payment in full". It doesn't always work and I have no idea what the law is in La. but what can in hurt? We do it quite often and usually send with a letter confirming that acceptance is payment in full and directing that the check be returned if they don't agree.
good luck.