You should go with a tire swing and eliminate the bracket on the rear door.A tire that size weighs to much for the rear door hinges.
For the bumper and tire carrier there is stuff like this.
Rugged Ridge RRC Rear Bumper with Hitch and Swingout Tire Carrier for 87-06 Jeep® Wrangler YJ & TJ - Quadratec
If you wanted to keep the 3rd brake light either mod the one you have or there is this.
Body Armor JK-5120 - Body Armor 3rd Brake Light Kit for 97-09 Jeep® Wrangler TJ, JK & Unlimited - Quadratec
The tire stuck out really far with the bracket on. Wont that eventually bend the tailgate and the hinges over time,regardless if I extended the rubber bumpers or not?
I put 33's on a YJ and it BENT THE TAILGATE.
The vibration will cause the tire carrier bracket to eventually break. In some cases, the tailgate will also exibit stress cracks.I'm running a 31" spare with an adapter, no extended bumpstops... is that gonna cause any serious problems?