I find TRAMP (https://www.emacswiki.org/emacs/TrampMode) invaluable in these situations. It lets you run shells/edit files on remote machines from within your local Emacs. There are a few quirks that you need to get used to, but it makes Emacs + a bunch of regular Linux boxes into something that feels very Plan-9-y.

In your case, you would want to look into the multihop settings that will let you open files and eshells on remote machines, but use an intermediate machine (your jump boxes) to get there.