If this is still an issue after you check David's theory about premature analyzing, another approach is to pre-populate and pre-analyze future tables. Something like this:
* disable autovac on the future table
* detach the table from the main partition
* insert a few hundred thousand rows into it, then run analyze on it
* can pull rows from a current table, or just use random data on a key column- whatever is enough to generate "good" stats
