It'll be a miracle if this judge finds the courage to order Obama to produce his original physical documents. As you said, they cannot hold up to expert examination.
If there were some way that these judges could be assured that a big “rollback” mess wouldn’t occur if he is determined to be ineligible, I think they’d be less inclined to try to cover up this major SNAFU in our system.
As it is, 4 years of signed laws, appointments, and executive orders would be up for legal challenge because they weren’t legally enacted.