I have been looking at the Watt Power Tester and some of its equivalents as I do want to find what voltage is getting through to the dometic refrigerator. ...
Did you mean to say what amperage is getting to the fridge?
Tim: I believe what you were suggesting instead of the current getting to the cigarette lighter socket was to test the running current used with the refrigerator's operation. I am assuming that the only way to use the shown tester would be to split the dometic power cable in 2 and twist and solder the connections to allow this inline display to be read properly.
Not the only way, but, correct. If you install the ammeter inline at the fridge you will be able to monitor amps, watts and kilowatt hours. Simple math... to convert the kWh to aHr you divide the kWh reading on the ammeter by the voltage of the source, your battery's voltage. That will tell you the aHr's used. You should use 13.3, or thereabouts, for the voltage if you are using your new LiFePo4 battery. If using a SLA battery use 12.3 volts (or thereabouts).
I know that this is something that is commonly done, but I don't know whether I would trust my wire connection skills to permanently stay in place. There always would be a weak point that if the fridge was pulled out of the camper without disconnecting it could break apart the wire connections. I don't know whether the benefit would out weigh the potential downside.
I am going to go out on a limb and say that your wire termination skills will produce a better connection than any 12v cigarette lighter socket. On my first trip with my first TD the plug vibrated out of the socket repeatedly. To the point every time I stopped I had to plug it back in.
In reading refrigerator testing forums I have heard another option which is a "kill a watt" current tester. The only thing is, I don't know how this might be used with DC instead of AC power.
The Kill-a-watt I have is for 110 volts only. A 12 volt ammeter is going to do the same thing, sort of.
I did a little research on how far 70 Amp hours would take me with the dometic refrigerator's rated 3.1 amps and did decide to bring back the AGM battery. After a lot of deliberation I ordered a 100 amp hour lithium battery; knowing the temperature related short comings that it has. I am doing the teardrop camping as a hobby and not having to spend large stretches of time in it so I believe that this might be a hopeful solution.
That will be an improvement. It will give you more reserve capacity. Just do some preplanning before you head out. Precool your fridge on 110 volt at home. Put cold items in the fridge, at home.
Charge your electronics during the day when the sun is shining on your panel. Conserve energy when you can. If you buy a six or twelve pack during your stay do not put it in your fridge unless it is cold.
It's all common sense stuff. Think about energy usage before and during every trip. Maybe that's a PITA but it will become routine and easy after a while.