I'm back and none the wiser about why I'm starting over, but the GP had a listen and is putting the referral in (again, for the first time). He said there could be a wait, but I'll hear something, at least. And I got my maintenance inhaler prescription refilled. So, success all around.
I love that we were on the way home with presvription in hand 20 minutes after my appointment was scheduled to begin, yet I didn't feel like they were rushing me through. He seemed genuinely concerned about sorting this out for me. Yay!