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How does this type of Platonism handle things like Beethoven's musical output? Is it claimed that the symphonies "existed" somewhere and Beethoven only discovered them (a rather Zen-like posture.)

I would suggest the mathematics is invented more along the lines of an artistic creation than it is discovered. Mathematics is generally invented to describe something in the "real world" so different people do get similar results.

As an example, I invented (for what seemed a good purpose at the time) the following sequences of numbers:
Pick a prime, (2,3,5,7...,etc); then first write the integers using that prime as a base; (1,2,3,4,5.... become 1,10,11,100,101 in base 2 or 1,2,10,11,12 in base 3 respectively); then "reflect" the number about the "decimal" point; (1,10,11,100 become .1, .01, .11 ,.001 or 1/2, 1/4, 3/4, 1/8, etc.); next take the resulting fraction and replace the numerator by the number such that numerator*replacement is congruent to 1 modulo the base; use the resulting fractions as the sequence: 1/2 => 1/2, 1/4 => 1/4, 3/16 => 11/16, etc.) I'm not sure what it would mean to say that this sequence "existed" prior to my building it. (Unfortunately, the sequence didn't have the properties I wanted.)

The speculation on Beethoven discovering his symphonies is fascinating to me - mostly because I perceive harmonics at the root of "all that there is" - just above the geometric. And, for those who insist on the plenitude argument ('everything that can exist, does') - it would have to be true that the information set of a Beethoven symphony exists physically and mathematically.

Mind wandering here... (LOL!)

With regard to your mathematical invention - perhaps someday it will be to a physicist, the necessary means to reveal a physical law. That is after all what happened when Einstein was able to pull a geometry off-the-shelf to explain relativity.

Ultimately, whether we see your work as a discovery (Plato) or an invention (Aristotle) - is a matter of personal irreconcilable worldviews. To me, you are a discoverer.