The “system” of chord names itself isn’t that bad I think. The difficulty arises when naming chords that aren’t in the typical triads+extensions format, and also from the many exceptions and special cases. Not the first time a neat theory concept explodes when confronted with reality. 
I don’t really mess with 12-tone rows/serialism and such, but the other concepts you named there I feel comfortable with. Ask me anything I guess!
Still on the topic of chords, here’s something you might like:
I have a pet peeve about the way the concept of “chord voicings” is usually explained. Many (otherwise very capable) music theory teachers will base their explanation on the idea that “chord voicings are variants of the same chord with the note in a different order”. The word “order” there always bothered me, as it’s not really a well-defined notion. What do you mean order? If I sing C4E4G4, and then sing G4E4C4, I sang the notes in a different order the second time, right? But those were the same voicing.
A better explanation (IMHO) begins by explicitly stating an idea that is pretty much always implicit: Modern/Western music theory always assumes something called “octave equivalence”. Notes that are one or more octaves apart are given the same name, even though they are actually different notes (of course). This is not a “truth” about music, just a helpful simplifying assumption.
On that assumption rests the concept of chord voicings. “C” as a chord name doesn’t tell you what octaves the notes should be in. So, many possible collections of notes share the same chord name, because they differ only by the octave(s) in which the notes are played. These are referred to as “voicings” of the same chord.
Example: E3 C4 G4 and C4 G4 E5 are different voicings of a “C” chord. “Spread voicings” specifically, since there is room between C and G for an E, which is not there, it’s been moved down or up an octave respectively. Spreading out the chord over a larger range.
Sometimes, there are names for different voicings. It’s often assumed for example that the letter name is also the lowest note you hear. If you want a different note as the bass you can put C/E for example, and that might refer to the first example above.
Another example is the one from the start of this thread. C6/9 and Am11 differ from each other in the exact same way that C and C/E does (which note is the root/bass). Chord extensions just happen to exist that describe the relationships of all the other notes both to C and to A. So you can write those instead of the slash notation.