Righty-ho, nothing like a real-world test to see what works. I happen to have a brand new 235/85 ST Maxx (on the large size as these sizes go, I understand) on my D1 spare wheel carrier, and can confirm it fits with a good half inch to spare underneath (pic 1).
I also have a 255/85 BFG M/T KO2 spare - also unused - and can confirm it ALMOST fits - but DOES NOT. It is literally only a mm or two away from clearing the bumper. I can actually force the rear door closed with it on and the tyre rubs along the bumper. Not damaging - actually the heavier spare (than stock) will be supported by the bumper, so if you don't mind having to shove the door closed with some effort, it might actually be a good thing! (pic 2). A few months of wear and it'd probably fit fine. Or even a little more deflated, but that might defeat the purpose of a spare, eh?
I can also confirm that flipping the spare tyre carrier through 180 degrees (a la D2 advice) probably won't work - the top and bottom holes are in the same place as far as I can see. The middle hole is offset, so it wouldn't flip without redrilling some holes anyway (pic 3). That seems to me to be the best option if you want to raise the bracket - take off the carrier bracket, and either drill fresh holes below the existing ones, or even use a round file to enlarge/extend the mounting holes downwards, so the bracket can be raised up 5mm or so, which should be enough to accept the 255/85 tyre. The rear door wiper in its resting position only clears the top of the bracket by an inch or so, however, so care would be needed.
Finally, there is plenty of clearance for both wheels between the carrier and the back of the door, in case anyone was interested. For offset reference my 235/85/16 wheel is a Wolf style, and the 255/85/16 is a Modular.