Could you get what you want with Unix job control? From inside e.g. emacs, hit control-z, and it should suspend the emacs process and you'll be back at the shell you started emacs from. When youre ready for more emacs (woo!), tell bash to "fg" and you'll be back in emacs.
The features of Qedit that I liked had more to do with editing functions and keybindings than suspending any processes, and running concurrent applications is sort of a non issue in BSD/Linux.
The default Qedit settings made columnar editing as easy as linear editing... You could copy/paste in a vertical manner, as well as the more normally seen horizontal method.
This facilitates ease of copying/pasting/deleting blocks of code without picking up, or affecting, other portions of code, whereas horizontal oriented block editing does not allow multi-line editing within set columns.
You get every column within a set of copied lines even though you only want a smaller block of text.
Perhaps emacs can do column based edits, or some other editor?
Both Emacs and Vim can do column and arbitrary rectangular area manipulations. Another old and popular editor in the DOS days was Brief, which could also do them.
Vim puts the terminal in raw mode, so ^Z sends ^Z instead of SIGSTOP. When Vim receives a ^Z, it shuts down ncurses, returns the terminal to a sensible state, and sends itself SIGSTOP. When it gets SIGCONT, it sets up ncurses and reconfigures the terminal the way it wants again.