Costa Rica with transatlantic legs in BA First Class you say, why here's a trip report that fits the bill...

BA First Class LHR-MIA-LHR, AA Y MIA-SJO-MIA, SANSA 9 seater SJO-Quepos-SJO

Okay, shamless plugging my trip report aside, I asked a similar question about where to connect in this thread:

Costa Rica - optimum way to get there

From memory, someone else started a thread last year where much the same discussion took place. We picked Miami in the end because the flights Miami-San Jose-Miami were much cheaper from there than DFW, IAH or MEX.

In terms of checking availability, forgive the question, but are you searching for 2 F seats in both the availability checker and booking engine? (Some people have been know to search for 1 seat rather than 2, forgetting that whilst it's a 2-4-1, there still needs to be 2 reward seats available.) The availability checker feeds into the booking engine so why not click through to see which flights it offers. If there is still a mismatch, ring BA. As for the return date, you may want to book your outbound now with a random return date and then move it at the real T-355.

Connecting in MIA - one rude immigration agent and a terrible Club America lounge aside, it's easy enough to connect in the building site known as MIA. It will almost certainly be better by next Christmas. DFW and IAH are much nicer but as I say, the prices were much higher and the flight times didn't work from DFW for us, or MEX for that matter.

Hope that helps.