We have a 15 gallon propane tank and it will last for weeks summer camping, running the fridge, hot water heater and stove/oven. During the winter, we can still go 10+ days, with the FAU burning the majority of propane. I have never really paid much attention to propane use other than in winter. We are set up for extended stays where I can feed the motor home propane through our BBQ "T" from an outside bottle if needed.
I would think a 5 gallon bottle should last a week running the fridge, cooking and hot water heater.
Granted we camp (Glamp - Class A MH) in mostly sub 90 degree temps, and mostly at elevations of 3-8000', but we do go to the Colorado river in summer at least once a year and it will be in the 105-115 range, and the fridge works great on propane. I do run a small interior fan to help circulate the air around the food, but it stays good and cold and we freeze water bottles for the LandCruiser ice chest each night. So no issues at all for us.
On our old Bounder motor home, it also had a Dometic, but a 3 way, but we never ran it on 12v. It also did not cool well when it was hot and humid. I fixed that by adding a small computer fan to the exterior vent area of the fridge. It turns out that Bounder/Fleetwood did not allow enough air circulation around the coil. It would work ok most of time, unless it was hot and humid, which caused it to freeze up and not cool worth a damm. The little fan made it work like it was in the arctic!
When it was not cooling well due to poor air circulation, it ran all the time and used considerably more propane. Maybe see how your venting looks. The fan was $10, add a switch, wire and an hour and your good to go. Maybe worth a try.
As for us running a compressor fridge, my wife likes her comforts, so we use a fair amount of 12v power, hence the panels and storage. Most of our trips are in the winter, so short days to recharge, or we are in the Sierra and get shaded by tree's most of the day, so we need lot's of storage for 7 day+ trips. We also use an invertor to run many a microwave, tv/satellite and coffee maker. We seldom run the generator, unless we have many days of no sun, snow or heavy tree shade. Even then, storage will take us at least a week.
It just seems a waste to replace something that is commonly used and that normally functions well in 10 of thousands of vehicles. I agree a compressor style is nice, but why when propane is quiet, easy and normally works well.
Either way, i hope this helps.
Doug