After delivering evidence and surviving the assault, more mechs begin to spawn while Taimi attempts to override the system. I destroyed all spawned enemies, and it never moved to the next phase. The levers never spawned, the room layout did not change, and no further dialogue happened. I left my character in the room for some time while I checked the known bug thread and wiki, and they were stuck in this particular area for over half an hour. After relogging and trying again, I was able to reproduce the circumstances again, but upon attempting it a third time (to try to take a video), it did not stall. I initially thought it may have been due to destroying the mechs while dialogue was still happening, but I did so all three times to attempt to reproduce, and it did not stall on the third attempt.
Either way, this didn't seem to be on the EoD known issues list from February or on the wiki, and there's no "story instance" section in the in-game bug reports (where I typically prefer to send things), so I'm posting it here.