I think I'd be sendng my medical certificate in now with a covering note explaining that you're still waiting for your registration document. Just say that you've had confirmation that you are now registered but the relevant document hasn't reached you yet and you didn't want to risk running out of time while you're waiting for it.

I'm sure they're used to people sending things in dribs and drabs as they come in because there's often a big discrepancy between the times it takes to collate all the different pieces of information together.