I think I'm finally getting the hang of this game. The levels are very difficult, I don't feel this game could work at all without the various built-in rewind options. In any case, I thought I'd help out by posting a demo that solves this room. I'll also post my solution in secret text.
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×The best tip I read above, that helps but not too much: don't use the bottom of this map.
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×Another hint not a giveaway: start on space 2 of the NE corner.
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×The next set of secret texts gives away my solution. I number the roaches in reading/crossword order, 1-11.
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×On your first move, stay still or rotate your sword, to allow roach 11 off a critical spot, then head left.
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×In many places (but not usually the big double-wide straightaways) you'll want to move diagonally to preserve more options for movement, yours and the roaches.
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×Wait on the first X for several turns so roach 9 doesn't go down the wrong passageway.
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×Continue left to the NW entrance. This allows roach 2 to get out of a trap, and also allows you to kill your first 4 roaches.
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×Proceed down the left spur, killing roach 7. However, you also need to go deep enough to trap roach 3 in a side-spit -- this is critical, so he doesn't get back in a place where you won't be able to get him out later.
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×Roaches 1, 7, 8, 9, and 10 should now all be dead, roaches 3 and 11 should now be trapped in new, easier to access spots. Head back to the right across the 2nd X. Don't worry, you'll be exiting in the NE corner, where you came in.
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×Make sure to not block off either roach walkway or your final exit to the NE, but make your way to the wide area on the E part of this map, killing roach 11 as you head down.
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×You'll need to go S far enough so roach 6 gets out of his trap, then N far enough so roach 5 gets over the hump, then S far enough so roach 5 gets past the last corner, then head up N. Note that you've now lost access to the bottom part of this map -- no problem.
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×Head back up to the NE exit. All 5 remaining roaches (2, 3, 4, 5, 6) should now drain up to your corner where you can kill them easily before exiting to solve the room.
See the attached file for my solve/demo.
-Rorke.