I used to work in a boat shop. The rule was we did not go under a boat, not fully on a trailer, unless it was supported by TWO independent ways, each one capable of supporting the boat by itself. Most of the boats we worked on had lifting rings, and we has a pair of chain hoists that used the lifting rings, and we would build a crib or box of longer 4 x 6 timbers to also go underneath the boat.
If you have the rotisserie, it would seem a no-brainer to leave it in place, and also use the taller jack stands in place. I too think is is a very good idea to tie then both together, ideally with a strut going diagonally from the bottom of one to the top of the other.