Steve
I also have a 2006 Monterey (Ventura) that had a failed Dometic absorption refrigerator just like yours.  I replaced it with the very popular Samsung 18 cf counter depth model.  It is a nice fit side to side, but requires a couple more inches vertical clearance.  At first I removed the cabinet above the fridge space and installed the Samsung (it is nice to have the high ceilings).  We used it that way for a year.  My wife did not like it that way.  She is a bit vertically challenged and could not see the top shelf of the fridge (the Samsung RF18 is a bottom freezer model).  So, when I had the opportunity, I took out the original floor of the fridge space and built supports as low as I could.  One of the Hydro-Hot registers and the vacuum port are below the fridge space and I did not want to relocate them.  I then put the original cabinet doors back on for cosmetic purposes above the Samsung fridge.  We do a lot of boondocking and I did not like having to leave the large 2000 watt inverter on all the time since it is a power hog even at idle.  So, I eventually installed a small 1000 watt pure sine wave inverter and dedicated transfer switch just for the Samsung.  It has now been 5 years and we are very happy with this unit.  I was surprised at how little power it uses.  If I can provide you any assistance should you decide to go this route, just let me know.
Richard
p.s.  If your Dometic cabinet is in good condition (mine was not), I believe J.C.Refrigeration makes a 12 volt powered compressor version cooling unit to retrofit to that box.  Good luck with whatever you choose to do.