For me, Fridays are usually better days to be off work than on Mondays. It also seems like most people have the ability to at least work a 1/2 day on Friday.
If it was a local contest, Sat/Sun would be fine. If I'm driving out to AZ, coming home early on Sunday works best.
I'm one of those people that likes to clean my smokers and all my gear the next day, so having Sunday to do that works great. I have found that if I don't get it done on Sunday, it sets until the following weekend. I just can't seem to do it after work during the week.
I know you want to get as many participants as possible, and it's hard to please everyone, but I think you gotta cater to the locals first. If people want to be there bad enough, they will find a way to make it no matter what the schedule is. So, having a killer contest seems to be the real key.
I think that was my 4 cents worth, but I'm up early and drink'in coffee, with not much else to do until the family wakes up