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.