Thanks for the reply!
Unfortunately, if the Steam overlay fails to load entirely, then the controller won’t use _any_ profile, be it mouse/keyboard, x-box, or otherwise. It’ll get stuck in its default “desktop” mode which isn’t usable for games, so gamepad emulation won’t help in this situation. However, turning on “show original” will get all types of profiles working, albeit without its Steam’s overlay being drawn in-game.
That said, your gamepad emulation suggestion did get me thinking about another vorpX feature I forgot about: the VR hotkeys should perfectly replace the Steam controller’s overlay. So the problem was solved anyway! :)
For anyone that runs into similar Steam controller problems: turning on “Show Overlay” can get controller profiles working. Steam’s in-game overlay won’t work (at least, consistently), but vorpX’s own hotkeys work great. (at least for Fallout: New Vegas, YMMV for other games)