Hi Fizzy
If you can get enough height on the engine lift, then I agree with Capnahab. Stripping it is not the best idea if you can avoid it.
My hoist is sturdy enough, but wouldn't lift a lathe high enough, so I moved a reasonable sized Denford lathe and a Horizon mill on a hired car transporter/trailer. The sort that hitches to a car, has a tilting bed, a winch and a full solid bed (ie, not one with just a non-structural central composite board strip). I did it single handed and without drama, but not both at the same time.
On both machines I made bars (twice the lathe width) with swivelling wheels on the end, which I bolted to the machine through the feet holes to make them stable and let me move them around OK.
So get it to the trailer, drop the bed, use the winch to get it so far up the bed (to the centre of the pivot point), wind the bed down, then position the lathe in the middle and make sure it's absolutely secure. Drop off is the reverse.
It's probably a bit over the top and unconventional for most, but it worked well for me and because the car trailers are long and wide, they are very stable.
BUT I warn again, not all trailers have the right construction…..
Cheers – Will