Put aside the recruiting talk for a moment. In the case of 1A, CBSA played only ONE 1A opponent all year prior to districts. Half of their schedule was against 3A & 4A opponents. To me that's a bigger advantage than potential/alleged recruiting.
Why not make a rule that your postseason classification is equal to that of the schools who make up the highest % of your regular season schedule? If you're a 1A team by enrollment and play 25% of games against 4A, 25% against 3A, 40% against 2A, & 10% against 1A, then you bump up to 2A since the highest % of games were played against 2A opponents.
However, I'd add the stipulation that if X% (i.e. 25%) of your regular season games are against teams higher than your classification, you bump up one class. So if you're 1A by enrollment and play 75% against 1A teams, 20% against 2A teams, & 5% against 3A teams, then you bump up to 2A since 25% of your games were against teams above your enrollment determined class.
This would treat private & public schools the same.