Thanks to a tip from wwwqwerty, we found out that Team Wildcard has released an update to their 3.40 LE firmware. The update is a patch that fixes some issues with the initial release of the custom firmware.

Here are the fixes for this version of 3.40* LE v2:

* Removed non-functional File Manager option in the Recovery menu
* In recovery, detects ms0:/PSP/GAME/RECOVERY/EBOOT.PBP and only launches it if it exists
* Fixed problems that kept UMDs from loading properly
* Added support for %__SCE__/__SCE__ homebrew naming style
* Re-enabled the use of GAME150 and GAME340, though you *DO NOT* need them.

Note, however, that you'll need to run this from 3.40* LE to get this patch to work. Also, Team Wildcard notes that if you're having an issue with the PSP not starting after you install, go into Recovery mode and disable all of your plugins.