I live in San Luis Obispo, California and am involved with a group of folks in a dinner group of a similar nature. Our set up is a bit different than yours. There are twelve people in our group. Toward the end of each month, we break out a blank calendar and pass it around. Each person signs up for a dinner each month.
Single people sign up once and couples sign up twice.
Generally, we meet Monday through Thursday to accomodate any weekend events or travel plans, though if someone wants to cook on the other days they just ask the group. It's usually no problem. We have very few rules and those we do have are looked at in a relaxed way. Each dinner is the complete and total responsibility of the host. He or she pays for it, prepares it and cleans up after it.