I think you can tow them short distances up to 1 mile without problems. Just put it in neutral and winch it up. Read your owners manual but I dont think winching it on to a trailer is considered towing.
My ZTR has to have the wheels disengaged to move it othewise it just slide the wheels but I have done that too on the grass, just dragged it back to the shop with the wheels sliding, didnt hurt anything. I know hydrostatic tractors will move without power though if in neutral and on a slope so I am sure you will have no problem loading it on a trailer if you have a strong enough winch.
I think that if I had to load it with the FEL down. I would load it backward and just let the FEL slide up on to the trailer. But if you could get your tow cable under the FEL bucket and hooked to the front axle or brush guard, then the force of towing it would raise the bucket up. You may have to put the loader valve control in the raise position to do this, once raised release the control and it should stay up if the valve doesnt leak down. Raising with A handyman jack under the bucket would do the same thing, again putting the controls in the raise position and keeping the valve open till you had jacked it up as high as you want, then return the control to neutral and it should stay.