If I was the Czar, for the two private schools classes I would just use their straight up enrollment (doubled if still single gender). Of the total amount of privates or non boundary schools, the 32 with the best records make the playoffs (same IHSA playoff points system to break time breakers) and the split is purely enrollment based. Biggest 16 in the Large bracket, the smallest 16 in the Small bracket.
Lucky for you this czar has the data to show this;
v2.0 corrected for data error that wasn't picking up DePaul and Routt Catholic. Boylan Catholic and one of Bloomington Central Catholic or Ottawa Marquette are bumped (they appear to be tied across all metrics). JCA up to large class (thank goodness)
Large Class
16 - Chicago (Westinghouse College Prep) at 1 - Chicago (Whitney Young)
15 - Burbank (St. Laurence) at 2 - Chicago (Marist)
14 - Chicago (Prosser) at 3 - West Chicago (Wheaton Academy)
13 - Chicago (Brother Rice) at 4 - LaGrange Park (Nazareth Academy)
12 - Lisle (Benet Academy) at 5 - Wilmette (Loyola Academy)
11 - Joliet (Catholic Academy) at 6 - Wheaton (St. Francis)
10 - Chicago (Mt. Carmel) at 7 - Chicago (St. Rita)
9 - Chicago (Simeon) at 8 - Oak Park (Fenwick)
Small Class
16 - Ottawa (Marquette)/Bloomington (Central Catholic) at 1 - Belleville (Althoff Catholic)
15 - Jacksonville (Routt) [Coop] at 2 - Quincy (Notre Dame)
14 - Peoria (Notre Dame) at 3 - Palos Heights (Chicago Christian)
13 - Chicago (C. Hope Academy) at 4 - Chicago (North Lawndale Charter)
12 - Springfield (Sacred Heart-Griffin) at 5 - Sterling (Newman Central Catholic)
11 - Chicago (King) at 6 - Lombard (Montini)
10 - Rockford (Lutheran) at 7 - Chicago (Agricultural Science)
9 - Chicago (DePaul) at 8 - Normal (University)
Out of Playoffs
One of Marquette/BCC
Rockford (Boylan Catholic)
Decatur (St. Teresa)
Chicago (Payton)
Aurora (Marmion Academy)
Chicago (Noble/Bulls)