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You might do well using an intermediary laying container, such as a Glad sandwich container (1.75" deep, 6" square container usable area). Fill it 80% with a medium grade vermiculite moistened with 6-8 oz of water. Let your crickets lay for 24 hours, if a moderate amount, such that no more than 20 crickets are laying per container at any one time. If more than that, leave the container there for less time. Too many crickets for too long will contaminate the laying medium with their droppings, and you will get mold issues during cricket egg incubation that will ruin the eggs. With heavy laying, such that crickets cover the entire laying surface, you can only leave the medium there for approximately 4-6 hours.
Snap on the lid when harvested, with a 1/8" air hole in it. If kept at 85-90 F, crickets hatch in 9-10 days.
Use some insecticide at the floor points where the ants got in. Good luck !