×Grab a bunch of soldier horns in the first cycle. Make sure you get the ones near the middle of the room, as they can trap queens. You can leave a few on the west as they can be useful to have later.

Head to the SW corner over the next cycle. Some soldiers should have taken care of queens in the NW corner, others will have killed the golems and be facing off against the first roach spawns. You basically want to be next to the bottom row of queens and just killing roaches while most of the queens run to the hot tiles.

You should hopefully be left with the queens on the bottom and 4 or 5 in the middle on the tunnel (If any are stuck on golem corpses, it's probably easier to restart and try to prevent that by doing random things to change soldiers. )
Head up north at an appropriate time, to send the central queebs south. Grab any remaining horns, then head to the S wall again. Final cleanup should be straightforward.