One does not have to do an "end run" around the Constitution to favor a policy that respects people of all faiths, including atheists, in public schools. Nor does one have to do an "end run" around the Constitution to argue in a court of law against the establishment of purely atheistic science in public schools.
But that's not what happened in this case. Had they tried to make that case honestly, we would be having a different discussion.
The board knew that their plan wouldn't pass Constitutional muster through the clear guidelines already set down by the Supreme Court. That's why they tried to hide their real motives, and that's why they tried to hide the money trail. They got caught lying about it, and that's what got them in real trouble - it showed their guilty consciences. They tried an end-run, and fell down in the attempt.
By the way, science doesn't "disrespect" people of faith. It isn't "atheistic." Science is science, its deals with the natural world, and it's neutral to religion.
Do you consider the statement "God is outside the purview of science" to be "neutral to religion?" I consider it to be atheistic, and I consider it to be worthy of consideration in public schools. More to the point, how does one know your assertion to be scientifically accurate without adopting your presuppositions?