This relative minor concern shifts the autoharp from FC to CG as a key signature emphasis. I believe I could improve the CG instrument, which is being rebuilt anyway to add fine tuners, by changing the bass tuning for a better key of D or A, but the chord layout requested doesn't really allow it, and authorities have already been selected. I'll save my breath with the customers at hand. I'm just the mechanic. Consider the following:
Eb----F7----C7---G7---D7---A7-----E7
--Bb----F-----C----G----D----A------E
----Gm---Dm----Am---Em---Bm----F#m---B7
To change the bass away from supporting F and C, suddenly the Bb chord is crippled and not worth playing as a tonic or key root chord. As a IV of F, the Bb chord would be passable, I think.
I believe what people should consider is that, when an instrument is stripped down, either to add fine tuners or during a full refurbishing, is a good time to drop the key of Bb, optimize for CGDA, and add diminished 7th chords as about the only chords worth having in the leftmost area that is so troublesome re harmonics, the chiming of strings with tones that don't belong to the chord regardless of felt damping pressure. One would be adding these dim7 chords partly because the retuning for more D and A would cripple the Bb chord, weaken the F, and pretty much rule out seriously playing in F or Bb. What happens in such a shift of key emphasis is that instead of finding Eb and Bb keys unsatisfying, to say the least, those transpose to Bb and F, moving everything down a chord button tier, all relative.
My own CGDA looks like the following, because after bar 15 (from the right) the harmonics ruin the more important chords. The dim7s are passable, because so many strings are open on those chord bars:
Edim7--F---G7---D7---A7-----E7
-Adim7---C----G----D----A------E
--Ddim7---Am---Em---Bm----F#m---B7
That's only 18. If I put the dim 7 chords all the way to the left, 19-21, they are fine, but the next three in are terrible. To the far left of the 18, I could still add the chords that were displaced by the dim7s at #16-18, but they will be a tier separated from related chords by the three dim7s. The tacked on chords are actually playable that way. I have tried it.
What I currently have though on two instruments in different key sets is a lockbar in that leftmost, otherwise empty tier. I have some chromatic numbers that rely heavily of open note playing for better effect. The lockbar is held down with my thumb, while playing with other fingers, the lockbar released when necessary, since it cannot be used when playing accidentals to the key signature. It cannot be actually locked, or I would be better off switching to a diatonic instrument. Therefore, a regular button and regular felt suffice. The catch is that I can only have one at best, because I have to pick the top or middle button row, depending on which position does the best with avoiding harmonics, which are to be avoided on a lockbar.
So, my CGDA has a G lockbar at the end of the treble row, while my EbBbFC chromatic has a Bb lockbar at the end of the middle row.
What I expect will come most often is a request for simply 21 chords, never mind any more advanced lockbar idea, so I suggest that the mainstream recommendation, with of course other approaches being valid too, be like the following:
Edim7---Bb-----F----G7---D7---A7-----E7
-Adim7----C7-----C----G----D----A------E
--Ddim7-----Dm----Am---Em---Bm----F#m---B7
This allows that the F chord occur before the 1/3 node harmonic, maintaining the quality of the key of C. The next (3) are merely nice-to-have but expected to be nowhere near as musical as the other keys, with C7 forming a triangle pattern with F and Bb, giving the key of F. Dm as I have experienced it in this layout is to be avoided. One could consider using that position for something else, but there would be no point unless tested to see if it sounded useful. In my work with Appalachian chord set locations, that bar position sits right over the 1/3 node harmonic across the bass strings. Chords farther to the left have some harmonics in higher stings but not a whole series that ruin the chord entirely. The #15-17 bar positions are usually the deal breakers on chord layouts, depending upon exactly where the chord set is installed relative to the strings.
Many of the US vintage 21 chord models, 1975-1983, except the Appalachian and Centurion, have the chord set about 1/2" farther out on the string area than newer imports, which use the Appalachian chord set location exclusively, tight to the anchor end. The chord bars should be set back that 1/2" toward the anchor end like the new instruments, so that two more chords can be fitted in before hitting the worst harmonics. Only then do you really get a chance to fit in as many as (4) truly useful keys. That also gives more room to play the high strings.
It doesn't matter whether or not one thinks there is a need for diminished chords. The leftward area after #15 is not good for much else except chords better suited for a diatonic like Major or minor 7ths.
These are generally new players, first time buyers, facing this situation, so they are accepting advice about what they are likely to need, but not from me. They already have a mentor before they get here. I didn't always agree but I endorse using three dim7 chords by default. I just wouldn't necessarily put them all the way to the left or fill up all 21 chord bar positions.
Part of the reason I don't use all 21 is because meantone tuning of even the mildest, sociable sort only supports 6 major keys before trying to use two notes for two widely varying scales. I can't use Bb, C7, or Gm on a CGDA-tuned instrument because I use the A# strings for an F#7 chord, either in E or Bm mostly, tuned far too low to serve as Bb on the other end of the chord set. I could use Equal Temperament but then I wouldn't like it well enough to play at all and am puzzled how others can find such a foul little bugger so enjoyable. It's not too bad if it's perfect, but what autoharp is in perfect tuning or for very long, especially with oversimplified tuning techniques?
So now I go back to the bench and do the thing as standard bass tuning, while the chord layout is as if someone is serious about playing in A. The key of A will sound better, moved inward but I am not sure it is worth it, whether it will sound good enough to actually be used much. I do know that the key of A on an optimized 21 chord instrument sounds wonderful. That has an A note in the bass, but there then is no pretense about playing in Bb or even seriously in F.
You have to give up something to get something. Take something away and you have to restore balance by adding something back. You cannot plan chord layouts entirely on paper. They have to prove out to sound good on a specific instrument, or you make a change. That all assumes that sounding good is important and that one can tell good from not good enough.
I believe the ultimate answer is always owning and carrying more than one instrument, but few start with more than one.