I've managed five. Interesting challenge
Click here to view the secret text
×1N : It's possible to leave the room, sparing the 4 roaches released from the right alcove
1N2W : Spare the brain, use the mimic to open the door
2W : Spare the brain
1S2W : Kill everything to open the green door. Before leaving the room, release a tar baby
2S : Spare the brain (and the roach queens)
I've ruled out 1N1W. My theory was kill one of the roach queens last, just after it lays eggs. Beethro laughs like the room is complete (or he would do if the Neather wasn't present) but the Neather doesn't budge, and the green door doesn't open.
I thought about maybe 2S1W being possible, if the Neather is keyed to run just for killing all the brains, but sparing the snakes, but I've not tried this one yet.