Headphone socket only connect to one channel?

I have two different model Sansa mp3 players that have the same problem: both do not play one channel. By putting a little pressure in one direction on the stem of the headphone jack, I can get the unheard channel going. I conclude from this experiment that the socket connection farthest in is bent just enough to prevent good contact with the tip of the jack.
Can anyone suggest a remedy for this problem? I can’t replace the socket (very tiny, and probably integrally molded to the case in a cheap manufacturing scheme). I tried using a dental pick to bend the contact, but this was fruitless (can’t see it in that tiny socket, and can’t find it by feeling around. My lockpick fu is very weak).