Perhaps the first level of the game should start closer to the nut in the campfire zone. This is an important zone to understand and shows wear on many guitars. Players then use that as the basis to venture into open wilderness, e.g., by using octave patterns to identify matching notes on different frets.
This very much! I wasted so much time trying to "memorize" the fretboard. It comes naturally by practicing music. Almost all of it began from knowing just the low E string and applying first octave patterns, then other intervals as I understood what they were. Without musical context, it's not really all that useful to know how to instantly name a note on a fret. Maybe finding octaves quickly, given a starting note, could be useful in the time-based game realm.