My tabs broke as well, quite close to the battery's lower corners. Then I discovered a reasonably hot surface to place the phone - my quite old Apple Airport Extreme. I warmed the phone for a couple of 3 minute sessions, that didn't loosen the glue but made it more malleable. Then proceeded to carefully pull the tab on the logic board's side with tweezers, which was a success. After that I could get an old ID card under the battery and push the other tab into itself. That done, the glue basically gave out and the battery was free.
So my advice would be to use some sort of heat before pulling on the tabs, which will make them a bit easier to work with. It does take some time but result counts, right?