When is your flight? If it is in the relatively distant future, they may very well open some F award seats in the future. Either keep a close eye on it or try EF alerts.
I have a similar situation - I asked for a consideration by the revenue management people. That was denied as was my appeal - so "begging" them to open a seat for you is not likely to happen but you could try.
BTW, they were obviously not impressed by my LT Plat status, so don't feel bad.