I also struck exactly this problem with my 2004 +8.The round disc sits on top of the wheel and is covered by the wheel cover. The disc immediately slides off when you lift the wheel into position.I have wire wheels and solved that part of the problem by securing the disc to the wheel with a cable tie. With alloys, some other method of holding in place may be required - double sided adhesive tape?.
My other problem that with a luggage rack and a very heavy wheel that won't stay in place, it was near impossible to line up the luggage rack with the hole in the cover with the hole in the metal disc with the threaded hole in the bracket. Initially I gave up and discarded the cover so that I could at least see what I was doing. But it is a very nice cover with the Morgan logo embroidered and I really wanted to use it. I had a SS bracket made. Simply a strip about 400 x 40 x 3 with about 20mm upturned at one end. This holds the wheel in the correct position over the bracket. Still not easy to mount the spare, but now possible.
Finally, purchased and carry a 12v compressor and gauge so that I now don't need to check the pressure of the spare.