I guess I should finally concentrate my effort and make a reply to this.
This challenge is not exactly easy, and can be quite fiddly, but basically it revolves around the fact of how brained roach queen moves:
A brain roach queen first find what's its prefered move if it's a brained roach. Then it flip this direction, and if it's not diagonal, point it towards the center of the room (note that due to the fact that DROD rooms have even width/height, this points to a tile corner).
If it's not possible, try vertical, then horizontal.
So, there are two ways to do it, one easy, one hard. The easy way is to
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×outrun the queens so they stop moving away from you
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×
enter from the North entrance
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×press the plate before roach queens can make it past the yellow door
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×the queens will now turn back to the tunnel because brain pathmap points them towards you now. Just wait for it and take appropriate timed stabs
and the hard way is to
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×force the roach queen into the plate chambers
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×you can do this at any entrance, but you'll need a roach flood for this, because you'll need to fiddle yourself some extra time
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×basically, hold an insane amount of roaches on a plate before running. If you're fast enough and the queens are at a good place, they'll get to the door and slide up inside before it closes.