The chances of getting of the alternate list are quite good, especially if you have good letters. The adcoms meet once every few weeks or so to review alternates and decide to whom they will offer an acceptance (if anyone). When they do so, they apparently read your letters aloud to the rest of the committee. So the way I see it, they liked your stats enough for an interview, this is where your letters shine.
So good luck, there is still plenty of time to be pulled off the alternate list, trust me.