P is sold as First Class. The order is FPAG in descending priority. C is sold as a Business Class fare. The order for Business is JCDIZ, again in descending priority.

C should map to some First Class fare as defined in the fare rules. Since they were sold together as one itinerary and are both the second-highest for their respective classes, I would guess your C fare would map to P. If that is the case, you should be able to SDC to a flight with P availability. I've never done this, so I don't know how knowledgeable agents are on these things.

Better information is probably buried somewhere in the thread that was linked above.