How about building a rear spare tire carrier using a hub, bearings and spindle to mount the tire on?
Then put the axle & hub on a crank down trailer jack. Like you'd find used in a 5th wheel or commercial trailer.
(I have one on my 30 foot flatbed for the heavy tongue that is 4 inches square.)
This would allow you to lower the tire and raise the rear of the trailer not only for maneuvering, but save your back by eliminating the need to pick the tire up to remount it on the carrier after a tire change. (Thinking of those bigger 36 and 37 inch vehicle matching bead lock tires.)
Yea it would be a little heavier, but the larger tire would make rolling on rocky or sandy ground a lot easier. Up hill or down hill.
I have a 5000 lb winch mounted on a receiver hitch tube with a 1" grade 8 pivot pin for side pulls.
Which would work well in this conversation.
I use it more for yard work than anything, but it goes camping with us. A handy tool!
(Once used it to pull our kayak up and down a cliff on the Buffalo River. Our Motorhome was parked at the campground on top of the cliffs.)(Been known to pull up downed tree to cut up for firewood.)
Off the subject of maneuvering
I've been wanting to build a tire carrier that tilt out and allow the tire to lay out flat above the ground about 32 inches, to make a make shift camper table. Maybe a hard shell spate tire cover or a round plywood table top set on the tire for it's table surface.
A little taller and you could have nice bar table just itching for some tall folding bar stools.