Could most of space inside these machines be filled with an inert liquid, perhaps built in as part of the cooling system, or cooled by a heavily armoured refrigeration system, so that most of the submersible was effectively incompressible?

Here is the statement from the HADES research team http://web.whoi.edu/hades/a-sad-day/

Was it operating at or near its limits? Article said it was 6 miles down, is it built go that low?