I personally wouldn't do it...I'd find a used 3/4 ton semi modern truck (you say you have a $12-14k budget) to use as the tow vehicle and have two trucks...best of both worlds.
The biggest problem I see is your short wheel base, a 6000# boat (I assume this is the total of both the boat and trailer) is more than likely at least 25' long and any cross wind or 18 wheeler passing you will have the tail wagging the dog...not good. Swapping the drive train out of the '55 will take 3-times longer than expected, a lot more money AND will devalue the truck in the end.
Mike B
