(i) Yes, I certainly think that your meta-question an appropriate question for meta. In general, I think that if someone doubts whether the question they have in mind is suitable for MO, then asking about it here is a fine thing to do, and probably makes for a more pleasant experience than asking at MO and having it closed.
(ii) Yes, I think your actual question is appropriate for MO. It's quite specialized, sure, but you have a precise question and you've put work into it finding an answer yourself.
(iii) Now that I've got this far, I can't resist giving you a couple of links that might answer your question. First, there's Eugenia Cheng and Aaron Lauda's instructions for "Build your own 5-associahedron". This doesn't show which trees go on which vertices, but Figure 7-G (p.194) of this does most of the job.
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