Wuss. I know your spare is bigger than stock, but you should be able to heft it up there. Just make sure CP's not around with the video cam. I was glad I was inside my closed garage, alone when I mounted my spare. It might have been embarassing otherwise.
Or get one of these.
http://www.predatormotorsports.com/index.asp?PageAction=VIEWPROD&ProdID=5
Teaka might have it cheaper.
Or, along the lines of a winch, custom fab a rear winch bumper, rig a pully on a flip up arm above the carrier and lift it up that way.