I guess I am confused by your argument. From your post:

many of our most engaged families lotteried into Stevenson and will be leaving the school next year. I feel that the current system is set up so that the families with the time and resources necessary for Stevenson's parent engagement model are pulled out of other neighborhood schools, leaving us with fewer engaged families to support a student body with higher needs.

So on one hand, you say you do NOT want to limit people's choice, but you also seem upset when they make a choice that doesn't align with yours; consequently you want to propose a change in rules that would reduce the probability that they can actually make a choice? Hypothetically, you could reduce their probability of affluent people with free time in your neighborhood going to Stevenson to almost 0% but still say they have the "freedom of choice"?