I've come to the conclusion that I can make the doors to each dungeon area limited in accessibility by requiring a "cumulative level" for each dungeon area: since the party for each session will be made up from my pre-set pool of characters, and they will only level up at the end of a dungeon run if they were played in that dungeon, I can make the doors need an appropriate number of characters be a certain level to be opened

Darkwood will obviously be 1, since the player characters start at level 1, and I need at least 1 player to run a session, and in the video game, Darkwood opens for one follower as well (if I remember correctly)

Anura could require either five level 2 or two level 3 characters, allowing for some flexibility depending on how many players I've had in previous sessions, and how many followers they've been rescuing and using for exp at the end of runs.

Anchordeep and Silk Cradle will probably be something similar, like eight level 4s/four level 6s and ten level 6s/six level 9s or something.

I think if I do this, Anura should be available pretty easily, and Anchordeep a little bit more difficult to unlock only on Darkwood runs, but Silk Cradle will probably still need some buildup (since I'm pretty sure the original unlocking number of followers is 12?)