I think you're referring to a "Solent" stay - an inner stay, very close to the main forestay. Unlike a cutter rig, where the inner stay might be several feet from the forestay, and you might choose to fly both foresails simultaneously. If you haven't already, do a little reading on Solent stay setups (e.g.
Practical Sailor's article).
Yes, I've added a synthetic solent to our Catalina 22, for exactly the use-case you're discussing (we already had the heavy-weather jib, and didn't want it to feel left out when we went to furling

. And no, I haven't tested the system in real heavy-weather conditions, nor have I written up the full installation yet. Someday...
With a Solent (again, unlike a cutter), you'll attach the stay very near the masthead (mine is ~8"). So you shouldn't need a running backstay (if the stay were attached, say, 4' below the masthead, you'd be putting a lot more bending force on the mast, and need to support it from behind).
For what it's worth, we find the extra stay and foredeck attachment point to work great for mast raising. And the Solent halyard holds a hammock chair over the foredeck at the dock. So at least it got us something.