No offense but I kind of get the impression you pretty much have your mind made up and you came on here to get people to back you. If I am wrong then I apologize but that is the feeling I am getting.
Always remember whatever happens in this case your players in the coming years are going to have birthdays, anniversaries, funerals, proms, etc... coming up. It would be nice to be in Coach May's shoes and not really have to worry about it. I wish I could be in that situation but let's face it - the vast majority of schools in the nation are not like that.
Your best bet is to use what someone said earlier about having a set amount of excused and unexcused absences. Once you reach them then you have some sort of punishment.
This way you are giving the kids enough rope to hang themselves if they are that way. This shows you are flexible yet have a system in place.
It's your team and you can do whatever you want. But remember whatever you do to do it equally and fairly. If not then you will fewer and fewer kids at your tryouts.