I removed the rubbery plastic that is used to secure the joints enough so that I had something to solder to (soldering iron melting and exacto surgery). Split the outer sheath wire into two equal groups and tin them to connect to the two points on the MagSafe. Solder your connections and use electrical tape on the unshielded wires to protect from shorts.
I used hot glue, making sure to apply at least the first large blob all once in one blast to ensure uniformity. In reality i think that I always pull on the cord to unplug the charger so I opted for hot glue hoping it would take better straight on yanks vs shrink tubing's side-to-side protection (who knows though). If you use heat shrink tubing instead (which I have had good results with in the past) make sure you slip it on before you start!
Congrats on fixing a problem Apple should have never had! Please send me your ideas on how to make this a more friendly process, I would be very interested.
Good Luck and I hope the new breed of chargers doesn't cost 79$ or fail so easily. Its curious to because this could be a potentially dangerous flaw too.