I have a
Yakima Backswing 4 for my 4Runner and it works great. I have no problems swinging the bikes to the side to allow the rear door to open. With the H3 and the rear spare this might be tight (even though it does allow lots of room between the door and the rack).
If the tire prevented the rack from mounting you might want to try this:
Hitch Extension .
Hope this helps.
Rob (Ipedog)