Update:
Today we gave notice (and passed!) and they confirmed our provisional booking for a month from today.
Glad it's all official now (besides the actually being married part). It was helpful to talk to the registrar (rather than the people manning the phones) and have her answer our questions.
She said we'll get a copy of our marriage certificate that day. They cost £4 the day of the ceremony. We can request more later, but they'll cost more.
So we can do the FLR(M) priority appointment soon after our ceremony!
