First off bury it. You don't even have to bury that shipping container very deep however the ground is your best insulation right off the bat so dig a trench and move that shipping container in there. You cannot just bury it.
I would definitely use a stepped trench and then carefully stacked stone around and build up walls. Getting some material to shore up the roof and then place at least a foot of dirt over the top. And I would definitely use a lot of biochar and amendments to the soil and turn the sun facing side into a garden which will help to keep the soil cool. You could always use the rocks and slowly start building rock walls and having the rocks support each other instead of pressing against the container. Definitely would be an excellent place to start hiding all those rocks that you're pulling out of garden areas and other places.
As to the mice problem!!!! Well actually you really should look into this opportunity. Especially if you have this kind of numbers putting up some traps and starting to farm these mice..... Yep mice are excellent pet food! And barn cats!!!! Lots and lots of barn cats.
Just whatever you do do not use poisons and look into the resetting traps!
By the way all those mice can be ground up and used as fish food for an aquaponics system. As well as black soldier fly larvae maggots!
Have you thought about running a small greenhouse with aquaponics?
Just like anything life has its own issues and nothing runs perfect.
However with a couple of modifications you are doing amazingly well and congratulations on getting the power back going!!!!
Merry Christmas happy holidays and I know with your positive attitude as well as tenacity you will achieve success.