Then some of our clients would have been disappointed by the timeout errors they had started seeing, if they happened to make a request at the very start of the migration ;)

We ran our migrations multiple times on test instances of our database, because we were worried about this exact issue. We optimized the migration to remove extraneous changes a few times in order to cut down the time taken. Also, 13 seconds was actually the upper bound of what we saw -- many times we ran it, it took closer to 9-10 seconds.