That's what I would do.

Another possibility is to place a piece of plywood next to it, leaning on the back of the trailer, jack/crane/lift the shed onto four moving dollys, then push with the help of friends.

I helped a friend do that to a huge dollhouse he sold to another mutual friend (the dollhouse was huge, i.e. kid sized... his daughters played in it until they were almost in their teens. I'd guess it was about 8'x10' base and maybe 6' high at the peak? We used six moving dollys.