I am not sure if this is the best way or even the right way of implementing the behavior I described in my question but it achieved what I intended so I will just post it as an answer:
I converted all the sub-menu items to "custom links" and assigned a url for each of the areas (e.g., menu item "discussion" would have the url ~/forums/discussion
and so on).
As for the Forums layer, I added a rule that reads url("~/forums*")
.
Lastly, I added the sub-menu (or the custom links I mentioned above) to one of the desired zones (LeftContent in my case) in the Forums layer. Now the sub-menu assigned to a zone in the Forums layer sticks and choosing any of the sub-menu items only refreshes the Content zone.