I know of an old guy who could not fit his boat and trailer in his garage, so he cut out a small opening in the bottom of the steel garage door for the hitch section to stick through. You could set it up kind of like a doggy door for a smaller dog and make a steel hinged swing up mini door that closes down over the small opening when the trailer is not in the garage or perhaps even a swing down cover box. If yours will already fit in the garage, and you just want more space, obviously this won't help.
With all the stories of things going wrong while towing a boat, I am thinking it may be best to leave it original from a safety, warranty, retained value and insurance perspective and just eat the extra space requirement. A commercial built trailer is expensive and likely an engineer designed it to meet government mandated standards. Cue the lawyers if something goes wrong while towing it that has liability attached to the situation, and you have modified the trailer in a critical way with your own design. I guess if you could find a factory built one with a swing or removal option, that would mitigate some concern. If it is a commercial swing hitch that is added I assume the manufactures must have done a lot of testing for safety and size, weight of boat etc. so I guess there is also that.
That said, I do know a guy who has one of the swing type on the trailer for is 17 foot Malibu, and he has never mentioned having any issues with it. However, his boat is a bit of a garage queen and does not get towed much at all and then for relatively short distances. I don't know if he had the trailer modified or if the swing option is factory.