First, I apologize. I misread your statement about including certain neighborhoods as exclusion to poorer groups. But, it doesn't change the outcome.
There is not a science to the drawing of boundaries lines, and given that it is individuals making the decision there will always be an arbitrary nature to the act. Also, attempting to influence and petition the decision makers will be a component. The sheer act of trying to get one's position heard is part of the process, and it is exactly what you were hoping would occur. The neighborhoods that were included through luck or influence were either lucky or influential.
As long as not made based on illegal principals, reducing the access of a minority group, or are not made by illegal means, through bribes or extortion, the boundaries will stand.
The same can be applied to the remaining slots. You may not like the lottery system, but as long as the system is legal to conduct and is neither discriminatory nor corrupt, the school could cast lots, throw shoes, or hold a lottery.
Your goal is to influence the decision makers, at the district level on how the boundaries were drawn and at the school level on how the slots were allotted. I would now lose the feign, but I would keep the advice, "It’s too bad your child will not be able to attend her neighborhood school. Your concern is valid. Present your concerns to the board; ask about adding portables; write to your local paper," and add, start looking for another acceptable school that is open for enrollment.
Also remember that most, not all, "good" schools are good because of the number of educated, involved parents. You child will have a "good" school experience given the level of commitment you have already displayed. And be careful. Most parents will say their experiences and emotions do not impact their children and most children are very aware of and are impacted by their parents’ emotional status. This event, if you are not careful, could impact your child’s first impression of the educational system.