Hi,
Something I've used before is a state machine, where you store the current state (in your case menu location) in the onboard EEPROM and use the reset on the ATTiny85 as your switch pin. In this case the each time the ATTiny restarts it will need to know where it was in the menu earlier, so it can act on the reset as a button press. Just have your pot on the other input therefore as before.
I published a trivial example in this post where the reset was used as the sole control for a bathroom shower timer. Hopefully that example will illustrate what I mean, and this helps.
Cheers ! Geoff