I'm sure you would win that bet. Now, as to just how to root out the wasteful spending, I'm at a loss. Those administrative costs are somebody's fat paycheck for doing little, and that someone usually has connections. Try to make some real cuts, and you get the kind of emotional ad campaigns you describe.
How much funding the school gets depends on who you ask. Much of the money is siphoned off at the state level, or, in the case of large districts, at that level. The money that actually gets down to the classroom level, where it can do some good, is a far cry from what is actually spent. What we need is less centralization, more local control, and a larger portion of the money going to those kids it's for. What we're getting is more centralization and federal as well as state control. We seriously need to get Uncle Sam out of the education business.
I can remember when our sales tax was 5%, instead of 7.5 to 8% depending on where you live, and the state income tax was not enough to justify withholding. Property taxes did come down with Proposition 13, at least for a while and for some of us, but sales and income taxes soared. Now, we pay more than ever, and the state can't balance its budget.
And that situation is mild compared to what happens at the federal level.
OK, end of rant about government spending.