The year I applied, went to annual meeting, at the party event the last night, ended up chatting with this random endo while standing in line for drinks, turned out he was there by himself, it was his first AAE in a while and none of this co-residents were there, his former PD happened to walk by and they had a little reunion (I'm just standing there awkwardly) and then he turned to me and said to his PD "This is redchesus, he's applying to your program!" PD (who I think was a little tipsy) grabbed my badge and looked at my name then said "good luck!" and wandered off. But I did get an interview there.
Not saying that this a sure-fire method, but it's the wildest way I got an "in"