OK, I found the other 2 dungeons and was able to get in, so it's my error, not a bug on the main issue here.
The icon changing to say "level 1" access when I'm actually in the battlefields is still very misleading. The explanation given that this is because there is only "one way out" of the battlefields is totally unsatisfactory. I would have to classify this portion of the issue as a bug, albeit a minor one.
My battlefield maps don't work properly, which was a contributing factor in not finding all 6 dungeons right away. When I save and quit and then come back, my battlefield maps are blacked out. As I move through the BF, large rectangles of the map open up all at once. Once a rectangle opens up, it properly displays the areas I have and have not yet explored. Also, BF maps do not zoom in or out for me at all. I have no map problems outside the BF's.