There is currently no way to have an analysis bracket end on a note and have another bracket begin from exactly that same note. To me thats actually a defect but I guess that wasn't planned in the first place.
Something like "c\stopGroup\startGroup" will not cause the bracket to actually end and another to begin but rather will combine both groups into one. Using voices does also not solve the problem because either the note will appear twice or, when a ghost note is used, the bracket will not span over it.
I've attached my unanswered email to the lilypond mailing list (with examples) and also here is a link to a question on stackoverflow concerning that topic https://stackoverflow.com/questions/45572579/lilypond-adjacent-analysis-brackets
Not only adjacent but also overlapping analysis brackets would be nice:
Overlapping ones are acutally possible by utilizing multiple voices.
Check for instance this example: http://lilypond.1069038.n5.nabble.com/Analysis-brackets-td45330.html
However, your syntax proposal would of course be a neat solution to this issue and to writing arbitrarily nested analysis brackets