I put a yakima kingpin 5 bike carrier on my truk. It has the ability to bend down but not far enough down to open the hatch. It has locks for the bikes and works just great except for what it souds like you want it to do. It will clear the rear tire just fine and fit the hitch just fine. But definetely not open.
I think you will need a hitch like this one -
but this could still possibly hit and they are heavy and expensive. I will look more closely at mine tonight and see if it looks like it would hit or not.