Thanks for the pointer... I ended up taking the easy road and just created a fake "forum" called "?New Posts, all Forums."
Gave it the link of
http://www.myforumname.com/forums/search.php?do=getnew
For "Act as Forum (Will act as category if no)" I checked no. (This way it doesn't actually show up as a forum.)
It is "Active" but not "Open."
And I set the Display Order so it's first on the list.
Now, it doesn't show up under "Site Areas" in the Forum Jump, it shows up under "Forums" -- but it works fine and was easy to implement. So I'm happy enough for now.
Thanks again!