Yes. As you say, there are a total of 6 dungeons in the Act II battlefield. I have completely explored the three level 1 dungeons and repeatedly trudged out to the more distant level 3 dungeons to verify that they are still locked. As one might expect, the entrances to the higher level dungeons are farther from the battlefield "home" area (where the traders are) and distant from the lower level entrances.
Maybe you could do me a small favor, if you still have a save game after you found the Level 3 battlefield key. Enter the battlefield, then click on the leave battlefield icon in the secondary skill menu. Exactly, what does it say?
Thanks, Lon