It looks perfect to me! You've done an awesome job, Nick!
And for the explanation: as stated before, there are two distinct "camps": one that places the first degree of a minor scale on "La", and one that places the first degree on "Do". I would advise using Do-based minor, because of two reasons:
1. It encourages learners to develop a good sense of tonality - what is the "home note"? (otherwise known as the "tonic" or the "first degree" of a scale) and how do the other notes refer to it? How are they placed, relative to that note? This also helps the ability to develop aural skills, recognising melodies and intervals "by ear" and eventually - with some training - being able to copy things by just hearing them. This should be the ultimate goal of Synthesia, even though it's not the one being directly advertised - to develop all musical ability in general (both practical and theoretical), by developing the ability to play the most universal instrument in music (the piano or keyboard).
2. Because Synthesia's primary method of teaching is visual, Do-based minor encourages learners to recognise when a key is changed, which discourages learning by rote, and instead encourages the learning and application of the principles and rules inherent in music. The problem with La-based minor is that if the key changes from a major to its relative minor, or the other way around, very little will change on the key labels (therefore, learners may not even recognise that there has been a key change), but with Do-based minor (which we have already set up the labels for), Do - the tonic note, the first degree - has to physically shift position to the tonic of the new key from wherever it was before. When people see that shift of Do from the tonic of one key, to the tonic of the next key, the reaction is immediate: "Oh right, the key has changed because Do has moved. I must get my hand in a new position, if required, and get my brain ready to recognise all the notes of this new key." The only snag is when parallel modulations are encountered (e.g. C Major to C Minor) because even though the key changes, the position of Do doesn't. This simply requires a little extra vigilance.
Using Movable Do, with Do-based minor will result in one set of Do-Re-Mi labels for both majors and minors:
Do (1), Ra (b2), Re (2), Me (3), Mi (#3), Fa (4), Fi (#4), Sol (5), Le (6), La (#6), Te (7), Ti (#7)
These are the names of the scale tones of all minor keys. As you can see, it already perfectly fits with our labels.
To illustrate this, let's take A minor.
A minor exists in three variations:
Harmonic minor - which is the same ascending and descending: A (1), B (2), C (3), D (4), E (5), F (6), G# (#7)
This would be expressed, using the list above, as: Do, Re, Me, Fa, Sol, Le, Ti
Melodic minor ascending: A (1), B (2), C (3), D (4), E (5), F# (#6), G# (#7)
Expressed: Do, Re, Me, Fa, Sol, La, Ti
Melodic minor descending (also known as the "natural minor"): A (1), G (7), F (6), E (5), D (4), C (3), B (2)
Expressed: Do, Te, Le, Sol, Fa, Me, Re
If you check them all against the labels you have for A, you'll find that they check out perfectly. Cross-checking the labels with the Wikipedia article works, too. It really is that easy.
"Ra", "Mi" and "Fi" are the only notes not covered by any minor scale, but in the case of Mi this is fine, since Mi stands for the third degree in a major key, so having a different one for the third in the minor key emphasises the fact that major and minor keys are inherently different and sound completely different, despite sharing key signatures. "Fi" is also fine, as it stays the same as the corresponding interval in the major keys and is generally far more useful and common as a scale tone than the lowered fifth ("Se"). To make the case for Ra (as opposed to "Di"), the lowered second degree is much more common than the raised first (both in theoretical applications and in written sheet music, as it is easier to sight read a progression of notes in a certain direction than static notes with changing accidentals). This makes the relationship between the first degree and the note directly above it easier to understand. Not only that, but many modes (which are the precursor to scales) use the lowered second. None use the raised first. As an added bonus, six out of seven of the modes will already work with our labels anyway, without needing any alteration.
It really is a one-size-fits-pretty-much-everything solution. It also works for blues scales, and due to the ability to automatically work with six of the seven modes, some jazz scales (which are based on the modes) also work with these labels too.
By the way, can I see the note labels (not the Do-Re-Mi labels) for A, please? I want to check that a mistake I made in the notes for A (which I've gone back and edited now) hasn't made it in to the labels. (The mistake was that during copy/pasting, I left in a Cb from another scale which obviously shouldn't be in any of the A scales.)
Regarding readability of labels, how about taking the idea behind the "rainbow colours" option and making it more functional? Such as, colouring all scale tones in red, and all non-scale tones in blue? That would provide a direct visual reference to scale tones, and would serve to be more useful than rainbow colours, I think. It just won't look as pretty. Don't get me wrong, though. Pretty is good too.