You don't need to remove the male crickets. You should be able to see the females stick their ovipositors (the middle/third antenae) into the soil to lay the eggs. I would set it up so I could swap out the bin for a new one to keep the process going.
you may want to put some screen over the dirt, the males will dig up the eggs and eat them - dont use the cloth screen, they will eat right threw it- just cut the center out of say like a small zip lock food thing, so you only have the rim, put the screen in, and snap on the lid
I just put a shallow food container of dirt, about 2'' deep, in the cricket bin under some egg cartons and have a heating mat under the bin so it stays
I leave the dirt in there for a few weeks, misting it with a little water every
Then, I remove the dirt laying container to a empty tub with another heating mat under it and just keep it damp.
It takes weeks for them to hatch and they are super tiny.
To water them, I get some paper towels, wet them, and roll them up into a cigar shape and stick it in the tub.
Last time I tried to hatch the brown banded cricks from Ghanns, I had no luck!! they either did not lay, or the eggs died.
I have been told (take with grain of salt) that the large crick farms erradiate them to make them sterile to keep people from
I leave the dirt bin, on top of a heating pad, in with the adults until I see the first pinheads begin to emerge (about 3 weeks).
I also put a layer of mesh tape (stuff used to repair holes in drywall) over the dirt and cover it with about 1/4" of soil. This makes a huge difference in the number of crickets you will eventually hatch as the males cannot get to the eggs and eat them.
Be sure to keep the dirt moist and the enclosure humidity high by misting the dirt a couple times a day. Also, removing old food before it goes bad is key to prevent die-off