@psywar - Congrats! Interestingly, I didn’t read that text as saying “if you take even one class ignoring your AP, then you can’t do advanced standing with the others” - it seemed to me that if you e.g. take Calculus in spite of your Calc AP, then your Calc AP itself is no longer counting toward any potential standing. So for a kid like yours (or mine 
) - with so many AP credits that they easily exceed P’s maximum, it seems that forfeiting some of their credit won’t matter. Now whether it still allows all prerequisites is another matter.
As I mentioned above, I’m annoyed by the way they make you do a semester of advanced standing, which would otherwise be a good compromise. MIT let me just finish with fall semester senior year, but Princeton won’t let our kids do that - they have to do a full junior and senior year and cut into sophomore year.
Integrated Science looked really interesting to us too, but DS picked HUM instead (unlikely you could do both and a BSE, it seemed to me). Your DS seems to have enough APs that even forfeiting the science ones, he could still do advanced standing with the others if I’m interpreting correctly (though obviously I’m a layperson as well!)…
My DS is entering with (all 5s except USH, a 4):
CalcBC, Stat, CS, PhysC(both parts), Chem, Bio, USH, Euro, World, Latin.
It seems likely that he’ll just take more classes and stay all four years, but I agree that the appeal of paying for one less year would be great.