How do I alter a partitioned table to partition off of a different column?

[mlake-nyt]

Hello, I'd like to alter an existing table that is partitioned with pg_partman.create_parent() on update_time, by inserting a new column, insertion_time, and partitioning off of insertion_time. It looks like if I want to partition on a different column, I need to create a new table (please correct me if I'm wrong).
So I:

1. create all new things: a new table with insertion_time and a new template
2. partition on insertion_time with pg partman via create_parent()
3. migrate the data from the original table to the new table via INSERT INTO new table FROM original table
4. DROP TABLE IF EXISTS original_table CASCADE; drop table original_template
5. rename the foreign keys, rename the new table, rename new template to original names (in that order)

However, my partitioned child tables do not rename. How do I rename the partitioned tables new_table_name_p2025_02, etc to original_table_name_p2025_02 via pg_partman?