I'd agree that in going from a keyboard to buttons getting
used to the diatonic thing "lack of all notes" was rather
difficult. Given the kind of music I chose to play, it wasn't
TOO big a problem, but quite an inconvenience when it came to
playing in odd keys, or ones for which I didn't happen to bring an instrument.

That's something I hope having a Streb MIDI melodeon will
help solve one day (see above).

Another tough thing is not having the notes you DO have
available without a simultaneous action of both right
hand and left arm. I think doubling on stringed instruments,
where every note is a combination of fret and pluck may
have helped. What helps even more is to (on multi-row
instruments) learn to row-cross. In more than half the
cases when playing on the 'home' row of either D(Em) or
G, the note I need if not available on the 'home' row is
readily available on the other row.

That's just kind of a case of 'knowing your scales.'

As with the Stradella system, knowledge of music theory
helps, especially when playing multi-row boxes. If you're
tuned in fourths (D/G, G/C, A/D, Bb/Eb) everything is built
on the 'circle of fifths' and the machine is really a 1/4/5
machine. And of course the relative minor of the inner row
is 'homed' on the draw (versus the press) on the outer row.
No, really. It works. Very well.

Same with playing an instrument tuned 'Irish' style, as
a B/C or C#/D or D/D#, or C#/D/D#. You need to understand
how scales are formed as a combination of naturals and
accidentals and how the notes of a particular scale will
be found on your particular 'system.' In these tunings,
the instrument is primarily a melody instrument, as fits
much of the music they are used for, as the stock basses
are nearly useless and even 'custom' arrangements such as
the McComisky system are of limited use.

The same applies, of course, to the Anglo concertina.

I'm surprised nobody has brought up any of the 'free bass'
systems which were somewhat popular a few years back. They
look like Stradella, but they don't make any chords by
themselves!