Ok, so if you break the flimsy part of the contact (like I did), here's the jerry-rig that worked for me:

Get a single piece of double-sided tape the size of the circuit board (I used a Scotch Adhesive Dot). Now cut it in half. Now take a piece of aluminum foil the same size. Put one half of the tape on one side of the foil but halfway hanging off the end of the foil. Now put the other half of the tape on the other side of the foil but on the other end of the foil. Now fold the foil twice: once each to adhere the foil to the other side of the tape. Now you have an S-shaped piece of foil but with aluminum exposed on both the top and bottom and also tape to hold it against both the battery and the contact surface. Stick this contraption with the aluminum touching the contact and the other side should neatly adhere to the battery, providing full contact. Also note, if you do this, you want to remove all the pre-existing adhesive.