We left our truck and trailer at Harbortown Marina in Ft. Pierce, Florida, in secure storage for three months this year. A nice boat ramp was less than a mile away, we launched the boat with me in it then Toni took the truck and trailer to Harbortown while I drove the boat over to fetch her. It worked very well for us. Ft. Pierce is a bit north of Stuart but it could be one option.
A good place to start would be to Google Stuart Marinas and make some phone calls. Good luck and good cruising.