Can't you just flip the battery pack around so that the side with the pigtail is up against the board (with the pigtail pulled out the top so it's out of the way)? If the tabs on the discharge tray aren't tall enough to reach the contacts on the individual cells when it's in thie orientation maybe try wedging some of those spare battery bars you have there vertically between the cells and the tabs on the discharger. There is assuredly an easy solution without resoldering your packs.