After dragging the plane in and out of the shed a few times, I decided to construct a tow bar to make the process a bit easier.
Bent it up out of some 0.064" scrap, attached an old Bunnings table leg to it and put a cross piece on the end. I thought it may have been too short, but just tested it and it works a treat.
Because it slides over the axle just inside the fork, it's easy to turn the plane too.