High Clearance rear bumper + Tuffy Security Box?

I'm thinking about going straight to a high clearance rear bumper for my Taco. I currently have the Tuffy Security box on both sides and wonder if they will still fit. They do hang well below the what looks to be the normal cut line but I wonder if they will just sit inside the sides of a bumper.

Does anyone have direct experience, success or failure, with any brand high clearance bumper and these boxes?

 

Are the tuffy boxes larger/deeper than the factory ones? The factory ones clear no sweat with some room to spare. For reference this picture is taken from the rear tire facing the rear.

 

Ah-Ha!

I think I might have interference with the bracing...

Two pics. #1 is as close to the same angle as yours as the wheel well plastic would allow. #2 is looking at the box from the rear/side.