Where it does help with the Catch-22 is that if you hold a medical, go in to renew and are denied, then you aren't automatically screwed. As long as it isn't an SI that they withdraw before it expires (or is otherwise revoked or suspended), you've satisfied the requirement of holding a medical at one time. If the condition is one that affects safety, then you have to be under a doctor's care, and presumably the doctor has to agree that you are safe to fly before you can fly. And you will have to certify to that effect after your next medical education course. But assuming you and your doctor agree you're safe, and it's not one of the conditions that still require an SI, you can go fly on your DL, denial notwithstanding.
What I'm wondering now is, can an amendment with the same wording be attached to a different bill before being voted on as an amendment to H.R. 22? Or are they stuck now? If they're stuck, it seems like they took a hail mary gamble with this thing, especially since there were several avenues open to get a highway extension before the recess.