The comps we usually do have grilling on Saturday, BBQ on Sunday and you can enter all or any for judging. You do need to still pay to enter for the day. You'd basically get zeros in the stuff you don't enter but they will accept, judge and award any category you turn in. If you did decide to do a day, maybe grab a few buddies and assign each a category. It's fun with a team and also cuts the costs down.
I'm not in your area so I don't have anything to add about specific competitions.