Ok, I am going to join the crowd. I just picked up a Hakko 808 desoldering tool a few weeks ago. Hadn't had the motivation to put it to use, but today I broke it out along with my mass of CPS2 boards that I was unsure of battery change dates and began the process. That tool is amazing! It makes such quick work of the solder points.
Have already replaced the battery in 3 boards successfully, but still have 3 left. Leaving SSF2T until last because it is the main one I did not want to die on me.