I would rather grind your entire boat to a powdered dust, carpet, tv's, and motors included, before I would want to lay on my back and sand all the bottom paint off the hull. Bottom paint is the nastiest, and most chemical laden material on the whole boat. And the older the boat, the less EPA, OHSA regulated the materials were. Complete breathing and skin coverage protection is a necessity. Was not that long ago, lead was used in bottom paints, then it was copper....neither of these in a dust form from your sander can be good for you to inhale all day. And the black paint on there now has probably penetrated the gel coat on the bottom to the point where you would end up removing all the gel trying to get the paint off, also not good.
That being said, I am going down the same path as your first response... pressure wash or soda blast the bottom to remove all that's possible, leaving the original gel bottom. Instead of an ablative paint, I would consider a shiny colored matched hard bottom paint. LOOK for a paint that can remain out of the water for periods of time, since you trailer. Some hard paints require it to remain wet to work. One hard coat of a good quality paint combined with trailer life, you may never paint it again. Hard paint has a slick shine that will not rub off or dissolve as does ablative paint, so less marks on docks or anything else at anything less than ramming speed impact. Prep work is most important so read each product (can) for prepping requirements.
want my professional opinion Ralph?......do what the first fella said.
Rusty