After a few days’ trial and error following Community posts, I stumbled across a solution:
Sign out of Messages/FaceTime/Game Center/etc. on all devices.
Sign in to Apple ID online (applied.Apple.com) and go to Sign-In and Security then open the Email & Phone Numbers page. Add new phone number (e.g. your ported number) even if it’s already listed.
Power off your devices.
Power on your phone. Open Settings>Phone>My Number. Remove the existing/temporary/incorrect number and replace it with your ported/correct number. Press Save and return to Settings.
Turn on Messages on your phone and tick against the number you added. It should verify/authenticate, but the email address may have a cogwheel turning.
Turn on Messages on your other devices, then FaceTime on your phone and other devices. This should verify/authenticate them.
Now, your correct/ported phone number should show as My Number on your phone and as the registered number for iMessages and FaceTime.
Best of luck.
It really shouldn’t be this difficult.