UPDATE mt_entry
SET entry_convert_breaks="textile_2"
WHERE entry_convert_breaks="textile_1"
A simple rebuild in Movable Type, and it’s all better now.
Problem solved
Fortunately, my Web space provider (Dreamhost) has the lovely phpMyAdmin interface enabled, so I was able to just run a big old SQL update to change everything to use the Textile 2 formatter instead of Textile 1: