Is this another case where science got the causation and correlation backwards? Is it not more likely that depressed people eat processed food rather then the other way around?
The best thing I've found so far in terms of somewhat "shelf stable" sources of fibre is dried figs (and dates to a lesser degree) and certain brands of high fibre digestive cookies.
Low fibre content in a frozen TV dinner seems obvious, but it seems less obvious when you say "practically anything other than a handful of items outside of the fresh fruits/vegetable section".
It does help I guess if you eat so much sugar and fibre helps mop it up and digest it slowly. But the solution isn't to eat more fibre, it's to eat less or no sugar.
A body can survive without glucose and burn fat for energy instead.