If the registrar is up to scratch, they will first look at your unspent leave and then at your COA. When they observe that you are out of time, they will refuse to conduct the ceremony,
That's not true. As long as an applicant has the COA, the registrar will marry them, regardless of their immigration status. That is the point of the COA, and following the JR last year (or was it the year before?) even people with no status (illegal entrants, overstayers etc) are being granted COA's and are being married.
In some cases it is possible to apply for spousal visas as an overstayer - <claim removed>. But the chances are that if you wait in the UK and apply on FLR (M) once your visa has expired that you will be refused and that you would have to try at appeal. We are seeing a drastic change in policy on this, as applications used to be approved if the period of overstay was less than 28 days.
I don't really see a point in trying to extend your stay. I'd be happy to discuss other options, including the one that hasn't yet been mentioned of staying to get married and then leaving to go home to apply for a spousal visa. I think that the main point of speaking to an advisor is so that you can discuss all the options open to you, which a community legal advisor may not think of.
Vicky