I tried to explain this earlier but my post didn't post...so trying again.
I used to work for a lab that used brine shrimp to feed the research fish. We used a setup like this (but larger)
It's basically a plywood rack that held inverted 2 liter bottles with the bottoms cut off. Rather than using the cap and drilling a hole and sealing the air tubing with silicone, we used drilled rubber stoppers (readily available on amazon) which allowed for easy cleaning and a tight seal. We had air piping all around the lab so we didn't use a pump like anyone doing this at home would but each of the bottles was hooked up to a air control valve mounted well above the water line that allowed us to turn the air off to the one bottle we were using to allow the shrimp to settle to the bottom and the egg shells float to the top. After 5-10 minutes, disconnect the air tube from the control valve and kink the tube so it doesn't drain until you've got it over a brine shrimp net over a bowl or bucket or whatever you want to use to catch the waste water. Drain it down enough to get the vast majority of the shrimp but leave the egg shells in the bottle. At this point you can either drain the rest of the bottle into your waste container or plug the tube back into the valve until you're ready to clean the bottle and restart the culture. Rinse the brine shrimp in the net into a clean container with fresh water so you can feed them to your fish easily...we used a ~2.5 mL dropper. As far as cleaning the setup and starting it back over, once it's completely drained, disassemble and rinse thoroughly with water only and wipe off any crud that might have accumulated. Reassemble and fill about 2/3 of the way with fresh water, turn the air back on and add salt (we used instant ocean) to 25ppt. Let that mix for a minute or two before you add the eggs...1/2 tsp per quart.
We had 4 bottles running at all times for the lab. We used one bottle for each of two feedings daily for several thousand fish (Fundulus heteroclitus, Danio rerio and one other I can't remember) and rotated which bottle was used for each feeding so they had ~48 hours to hatch and grow before we used them. Even after feeding everybody we still frequently had a lot left over that I took home to feed my fish periodically so you may want to use a smaller setup or use less eggs per batch so you don't toss out a ton.
Hope this all makes sense!