Here's the situation:

The Mrs. & I are flying JFK-LHR-ORY next week, with an almost 6 hour layover in LHR en-route. We are in CW/CE, and while I am booked in a standard J ticket, her ticket is a complete mileage redemption. We are both Silver (and I am turning Gold with the return from this trip).

I just spoke with BAEC and they said that there are no CE redemption seats available on the earlier flights LHR-ORY on that particular day, but there are several paid CE seats left.

What is our best shot to getting on an earlier flight? Do we see what can be done in JFK, or is it better to wait until we get to LHR and try this from the lounge (if so, which one has the nicer agents)? Or from a customer service desk in T5? Or just try at the gate of the earlier flight??

Anything in particular we should try to say and/or do??

I have NEVER had luck doing this, but I am usually on a book & upgrade ticket and traveling alone, so they've had little motivation to help me.