I've watched Mexican Pangas which are also a dory, do this near Todos Santos, in Baja. The wait for just the right waves and run right up on the sand. I don't plan on trying this with Mistaya.
Those videos help me understand my trailer better - thanks for posting both of them!
I've got two spares (on on each side) but they can also flip down into position to roll like the first video... and I also have an alternate extended tongue that adds at least ten feet or so of reach.
I have watched the Pacific City Dory fleet do the beach launch and landings for years. Fun to watch, but don't think I will do it with SleepyC. In Aquatics Class in college we did it with a rowing dory. A bity moooorrre work, but with 6 rowers, (Oarsmen) it was great fun.