Had the same problem if you pull on the connector to remove a battery and it does not want to budge stop there before you tear out the connector . Pushing from the bottom is a good idea I just changed my battery it was swollen however that is not what seams to hold the battery in as much as the sticky label . Gave a quick shot of wd 40 down the sides of the battery let is soak down 15 min . I used a very thin machinest ruler and gently slid it down both sides being carefully not to damage the battery. When I seen the battery can move a little then I gentle wiggled it out .
No worries if a little wd 40 will not damage electronics if a little splashes on the board . I just wipe the inside of the battery holder before putting the new battery in .
Don't over soak the area.