Going to provide a demo here, and a rough description of what I did. This was indeed pretty tough.
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×First thing I did was make a passage from the lower left to the brain. This took some wrangling. Then I cleared out most of the roaches and killed the brain.
I timed the brain kill so the southeast queen escaped to the corner. Then I was able to hookshot to the south wall, hook her, move her, and hook back (having already given myself a path to hook back. I cleared out a diagonal path to her new corner, and hooked her from there (timing the shot for Turn 30 to prevent her from spawning) and then chased her to the middle for the kill.
After doing that, I made a run for the NE corner, hooked the NW queen and timed things so I chased the NE queen out of her nook, getting both those queens in their corners. Then I focused on clearing out the roaches in spots with no spawns, so they wouldn't get in my way later.
After flailing about and trying several different approaches, what worked was going for the queen in the southwest, first clearing out most of the roach spawns and then leading the rest to a spot where they wouldn't get in the way when I hooked her. I ended up leading her to the northwest before chasing her to the middle. Then I cleared out the roaches on that side. After that I just had one corner left, so it wasn't too bad to improvise.
It's important to note here that you do not want to open a path to where roaches are spawning until you're preparing to go after the queen(s) spawning them. This is vital to keeping the roaches in a controlled pattern where you won't have to face more than two at a time. Also, if a roach is under your sword, you can hookshot and you'll still kill it, which can be useful as a time save by letting you hook multiple roaches in a row.