I tried LovaP48's solution, but no matter how I fiddled with movement order I was always at least 2 moves short of the exit.
I don't know how to even begin to set up kikuchiyo's solution. Four roaches along that wall after the queens are dead just seems impossible, never mind putting them there in reverse order.
So I went back to one of my own ideas and got it to work.
Click here to view the secret text
×Put the queen inside the box. Nine roaches are enough if every one of them has to cross the same tile.
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he/him
~170th Skywatcher