Aforementioned stranger speaking. I've pretty much isolated the problem, but this will require some technical jargon that you can pass on to your grease--I mean--code monkeys.
It appears to be a glitch with the transport tubes, where a client will enter a tube, but the other clients in the room do not properly compute the signal from the server saying that the first client has moved. For example: Players 1 and 2 are in the same section of the labs, and can interact with no issue. But if Player 1 uses a tube, Player 2 will not see the transfer, but instead will see Player 1 "stuck" in the end that they entered. If Player 1 transfers back to their "starting" point in the tube system, Player 2 will again see them properly. This seems to be what happened with me and Ms. Cartbridge: When I arrived in "section 1", her computer did not recognize my transfer to "section 2" and to "section 3", where she was waiting. But because she was already there, my computer did notice her, allowing me to follow her around almost like a ghost. (...Made me feel like kind of a creep once I thought about it. )
But here's the catch: Whenever a client re-enters the room (either through the main entrance or through exiting battle) it sort of "resets", allowing said client to see the other clients in their proper locations. This is how I met up with Ms. Cartbridge: I started a battle in the same section she was in, and thus, she was able to see the dust cloud and join in. Then when we won the battle and re-entered the room, her client reset, allowing her to see me in my "true" location. Meeting in battle like this could be used as a workaround until the glitch can be fixed.
Honestly, though, I kind of saw it as an unintentional "extra puzzle" for me to solve.