Even though it never was going to work, I tried it.
The Steam Overlay only runs when the game is launched from Steam, and in most cases, will carry over from launcher to game. Adding cRPG as a non-Steam game worked for previous versions, so I am asking the devs to restore this functionality, it's pretty much a requirement for me to have.
Fixing this is easy. All you have to do is download the
Warband Script Enhancer and run the WSELoader.exe as a Non-Steam game. Now all I have to do is run the cRPG launcher every so often to check for updates, which isn't too hard. Since the Warband Script Enhancer is what is needed to run the game, not even the "Please use the Launcher" message pops up.
I am satisfied with this fix.