i dont think you will have a problem with people locking themselves to raids if you dont raid on tuesday. If the raid times are wednesday and thursday, people understand thats when you raid. Tuesday would just be reset day, not a raid day. It honestly shouldnt have an effect. At this point, you have to pick the lesser of the two evils. for example...if 1 person cant make fridays, and 5 cant make mondays....you would pick friday to raid as you would be missing less people.
my 2 cents