The current new game plus system seems to pre-maturely grant access to the random encounter dungeons, and give them priority over the story dungeons, thus halting the Newgame + progress.
I’ve identified the issue and will add the appropriate patch soon. (It’s a pretty small adjustment at that.)
Sorry for the inconvenience.
I’ve only now had a chance to fully check the patch and I found 1 more issue that locks out the Treesea levels.
(Some interludes depend on stage clear data.)
I’ll be thoroughly checking the new version this weekend to create an updated version.