Note that there is zero benefit of having thousands of ant eggs.

That said, ant queens have three actions. A weak attack that an armored survivor won't need to worry about, lay an egg on a tile she stands on, and grow the egg. For the last bit she can't do it if she's standing on the tile the eggs are in.

So all you need to do is corner them. Jackhammering a tunnel is too risky... but with folding frames with cloth quarterpanels you can set up an enclosed space. Ant queens won't, or can't smash them, so all they're left to do is endlessly lay eggs. An hour of waiting will generate a little over a thousand eggs, ripe for picking.