Well hot damn!
That'd certainly be getting a huge range out of the unit. For this game I'd ideally want it to be as accessible as possible while still being involved with actual music and not totally just hitting buttons and hearing sounds (though, a somewhat developed musical ear is necessary for replicating the notes that the birds sing so that would have to be made a bit easier I think). Your idea would definitely help it be a more comprehensive musical tool/toy, but for what I have in mind right now, I think it might tip the scales to be a bit too complex on that front.
Ultimately I figured that the single scale of from F to F (F# if you raise that octave note, but that's a pretty useless note unfortunately as I don't plan on doing any flat 9 chords) is the best option. By having each button be a single note, I thought it's easier to remember the controls. And the only notes that are not a single button are hopefully intuitive since the player is pressing up or down to raise or lower that note's pitch.
Having A and B switch the the 4 and 5 triads+octaves would be more easily grasped for musicians, but I think it would be a bit tough to understand if the player doesn't know any music theory. Musicians would know how those notes are relative to not only the chord but the key as well and would have an easier time grasping what combinations are needed for a melody, but I imagine non-musicians would be confused as to how to put those all together. Regardless of musical familiarity, having the range of notes from say F4 all of the way up to C6 would invite a wide range of melodic options and anyone would be hard pressed to learn all of those different combinations, especially when 2/3 of the available playable notes are a combination of two buttons.
Keeping the available notes (mostly) contained in the octave allow for a set of less overwhelming (though certainly more restrictive) options. I imagine it'd be more comfortable for newcomers seeing as there isn't a plethora of puzzle pieces in front of them when attempting to hear what notes the birds are singing. And as a musician, this octave restriction certainly made for a more challenging writing task! I wrote out the melodies and counter point for the fully designed game where the player learns new melodies during the day and night of each season (day is melody, night is the counterpoint).
Since we are well in the weeds at this point, I'll post the notation of the composition here below so you can see what I mean. I tried my best to replicate the melodic lines from actual birds of the respective seasons.
Ideally, if I had all of the time in the world to make this game, the family band would play together and would play all of the parts that the player is able to learn during the timeframe. A hastily put together version of this was made for the end credits song of the jam version of this game. So if you got to the end, this is the song that plays:
