Vartz,
I have a pelican 1600 case that I built last year. I am running two duracell's from Battery Plus (or Bulbs and connectors plus or some such now). They are the DURDC12-35J. I think one would fit in your case, but upright with the case laying flat they need about 7.5" of headroom. The folks here suggest that these duracell batteries are branded quality batteries, and mine have held up great for one year.
I had to create a frame work our of wood to "bolt" them down, as they are very heavy. I have my batteries mounted in the back of the case, and all of my accessory connections are inside, mounted on a board, facing up. No connections pass through to the outside of the case, like you have set up. I figured that all of the accessory plug-ins would take up a lot of internal case space, if surface mounted to the sides of the case. I do have to crack my case a smidge to rum my solar wires in, and fridge wire out, but I have not had any water problems, in use.
I am hoping the batteries will last a few years, and I can replace them with what you were trying to accomplish with the lithium. My case needs a diet, in a big way.
Good luck, and try and not beat yourself up too badly. This solar/12 volt stuff is tons of fun, but can be very confusing at times.
Craig