I understand your intent to eliminate bias, but "blind" selection would lead to a lot more mistakes than bias would. There is a reason EMD, Mishawaka, Bellmont et al return to team state nearly every year, even when they only return 5 or 6 starters. They are well established, deep programs, and their reserves could most often be wrestling varsity on other squads.
Just to illustrate, if you took the name "Mater Dei" off and reported that a team had only 1 returning state place-winner and 2 other qualifiers, that team wouldn't even be under consideration for an invitation. But is there anyone who really thinks Mater Dei won't be in the top 6 or 8 teams of their class this year?