Well, I thought, let’s go the other way then: upgrade Moodle first and then backtrack to PHP.
But Moodle 3.3 can’t go straight to 3.9 (which is the LTS I’m hoping to get it to) – 3.3 can only go as far as 3.5 – and Moodle and PHP documentation doesn’t say whether 3.5 will work with the existing PHP 7.0; time to take a gamble …
… and it paid off. Following these steps Moodle was upgraded to 3.5 and it worked with PHP 7.0
Then the upgrade to PHP 7.4 went smoothly.