The overall diameter is less than 5mm larger than stock, so I'm going to say that the spare wheel well has room for 2.5mm per side for the clearance. I think your issue will be with the width. That 285 tyre is over an inch wider than the stocker and I doubt that the load floor would sit right with it there. It's been awhile since I looked under there so don't take my word for it. Go look at your truck and see if there is 1" of room to give.
I have been considering getting someone to enlarge my wheel well and I think it could be done. There isn't a lot of room but if you had someone cut the base and sides out some gussets could be welded in to make it bigger. I want to carry a same size spare when I put Cooper Zeons on and this would be the only good way I can see.
The rear muffler is large though and may get in the way. I was also considering taking that off and replacing it with two smaller silencers there to give more room.
It would be quite an operation but it may be an option?