Have you got any parastic 12 V loads somewhere like tv or microwave (someone said recently some micros have a 12V circuit)? Could be a few things adding up to 11+ amps. I'd look or those and shut them off or disconnect them. Then turn off (unplug fuse) or disconnect any other known 12V loads like the fridge and recheck the draw.
With an DC ammeter, you should be able to unplug one 12V fuse at a time and look for a current draw on each of the 12V circuits. Just poke the test leads into the fuse sockets. If nothing there, then you have a problem somewhere between the battery and converter.
11.7 amps is about 140 watts of power and would be a lot if it's a fault somewhere and the heat is concentrated in one spot. (Try holding a 100W light bulb.) You might even consider renting an infrared heat sensor gun and looking for a hot spot.
On our TT, I discovered that the heavy gauge wire under the TT going from the battery to converter was missing a grommet through one of the holes in the steel frame. Could have eventually worn through the insulation causing a short. If you haven't yet, you might want to look at the 12V wiring under your unit.
Gil & Deb & Dougal the Springer Spaniel