Yep, chances are better if they get mated more often, but the girls have a way of storing sperm for a few weeks so unlike mammals, their timing doesn't have to be just right.
Just collect up the eggs, don't wash them to preserve the bacteria blocking bloom, and put them in a carton air cell side up. If they have any dirt on them, just brush it off. If it is really dirty, and you do choose to wash the eggs, do it under water warmer than the egg. Ideally, about 15C or so and something like 80% humidity is the best to store them at, but room temperature for a week to 10 days is also fine. Hatch rate just goes down past about 10 days of storage, but that said, I've hatched eggs stored over a month. Just put the carton in a plastic bag to keep evaporation down, and tilt the eggs every few days to ensure the yolk doesn't stick to the shell.
You do want to collect them and set them at the same time, because else you may risk the developing ones chances by having to up the humidity for the ones hatching. If you want to do a staggered hatch, you'd ideally have two incubators, one for incubating days 1-18, and one for hatching days 19-21/22.
I'd just collect up 2 weeks of eggs, set them all on a Monday for a Sunday hatch so you can watch them, wait two weeks, start collecting again for 2 weeks and repeat the hatching cycle. Granted, you might run into a problem of maintaining 5 brooders of a dozen chicks a pop each a month apart!
