Good luck in finding a boat that can take your father or both of you as crew. You are suggesting a lengthy time aboard a rather large vessel. Most cruising boats are actually not quite that big, though some are. A "first trip" of that length of time is actually a little risky as a good adventure for an elderly person.
You might alternatively consider a (crewed) charter vessel to obtain the sort of experience you'd like for your father's birthday.
Another more "organic" way of finding your way onto a boat? You might consider linking up with your local yacht club (Fort Meyers Florida?) to try and find a skipper who would be willing to have you two along as crew. Volunteering to be "rail meat" during the (usually weekly and casual) races is pretty much a good way to learn more about sailing and to get into the good graces of the local skippers.
Finally, something that may really go far in achieving your father's crew dreams is to get him some sailing instruction on-the-water on an actual cruising boat. That would be an awesome gift. He can pass the classes for certification at a variety of levels (ASA or RYA) and will then be pretty appealing as crew for cruising skippers. Food for thought. There are many excellent sailing instructors to choose from. For example, I know of a well qualified young couple (both USCG Capt) who could take you and your dad along with up to 2 other students on their cruising boat for instruction. Here is a link to their site Sail Training Expeditions - Sailing School Coastal & Offshore
Again, best of luck to you and your dad!