I don't think solving the funding issue would directly solve the performance issue because this is a problem with multiple variables like you have mentioned.
When we talk about stable 2 parent households we need to consider the fact that many black and Hispanic families are torn apart due to the higher incarceration rates for black and Hispanics when compared to whites, even for doing the same crime. When you split a family apart, even for a few years, and especially during the formative years of a child's life this will have a detrimental impact on their lives.
High income and the ability to afford tutors is also affected by not only education (as college educated workers earn more) but again by incarnation: if your husband is in jail you've lost his income, how can you afford a tutor? Especially if you don't have a great job due to your own struggles.
Even when looking at health there are discrepancies among the races that is affected by institutional racism: look at Flint, MI. Those kids are not going to perform as well as their peers down the road no matter what. Minority neighborhoods are also flooded with fast food chains because these corporations have made it clear that they are targeting these populations.
There are so many factors that we as Americans need to deal with, it's like placing whack a mole or untangling yarn that has been woven for hundreds of years. Almost every aspect of our day to day lives are affected by the policies of our past. We need to study them deeply and figure out a plan of action or we will continue to plug our fingers into the hole until another one springs up.