Have you tried locating a "weekender" refrigerator?  These already fit directly behind the passenger seat.  Dometic still sells a similar model and I believe it is also available with a LP option.

  Date:    Sat, 25 Feb 2006 11:31:25 -0700
From:    Jeffrey Olson <jjolson@GWTC.NET>
Subject: Cooling units for homemade fridge

Hopefully this isn't off topic.  I apologize if it is.

Has anyone bought the cooling unit for a 12v/LP fridge and installed it
on a homemade insulated box and cabinet? (I'm thinking behind passenger
seat)  If so, any practice wisdom to share?

Jeff
martin, SD