My goal is to be able to run the entire trailer using battery power if no electricity is available.
First, this requires that all equipment can run from 12 volt DC. I found Spectre brand monitors that run on 12V, and my laptop can run from 12V. Of course all the scope equipment and mount can run 12V. The trailer is already suited to run lights, water pump, refrigerator, and furnace from 12V and propane.
I found a toolbox that mounts on the trailer A frame tongue and holds 5 deep cycle batteries, giving me a total of 450 amp-hours of power. This should be enough to run several evenings.