I could see and edit to the venture mechanic that saying you can go into the dungeon or the "labyrinth", but there's still the issues of "can I be in both at the same time?" "can I leave the labyrinth at will and go into another dungeon?" "can the labyrinth randomly have exits show up that give you the choice to leave or keep going"
I agree that its nice to have more reason to design with venture than to have two completely separate mechanics. Its just a bunch of design hurdles to make them work smoothly.
I think the challenge here is that flavorfully it wants to be a dungeon but its to be mechanically different enough that gameplay wise it will want to be something else to handle rules differences.
-You'll never trigger payoffs for completing dungeons
-Once you start the "endless dungeon", are you stuck with it forever? You can never again choose to start a "normal" dungeo
The idea of a deck with randomized dungeons is cool and you could feasibly have more complicated effects if each card only needed 2-3 rooms. Also, power level for effects can be higher since you're not choosing the dungeon yourself. You could even share the deck so each person's endless dungeon is coming from the same source.
Again, the flavor is spot on, its just the meshing with the current play design that is a challenge. Maybe make it a "Labyrinth" instead and then you can make the rules to suit its specific needs?