The key tactical point that let me start making progress:
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×Due to positioning and overlap with other queens, killing some queens will reduce the spawns by 3 while killing other queens will only reduce it by 2. So, to make the most of your time, you want to try to sneak in some kills of 3-spawn queens at the start.
If you need more help, here are the first few queens I killed, numbered in order:
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×
Enter with sword NW.
And if you're still stuck, here's a full spoiler for the route I took to get the spawns below 30:
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1 reused because I only get nine labels.
You have to kill roaches for a while between 6 and 7 before you get an opportunity to advance safely, but it happens. You may also find you get stuck at the door between 8 and 9, but just swing your sword back and forth for a little bit and movement order will let you advance fairly soon.
