What legal machinations could Obama use to frustrate the Grand Jury's ability to actually get these important documents?
A grand jury’s subpoena can be frustrated by an appeal to a Judge. There is a process where a subpoena can be appealed if it violates other established legal rules (like attorney / client privilege) or if it is unreasonable (produce 100,000 pages in two days). I suspect that Obama would want to claim that the grand jury does not have the authority, is not the venue to resolve, etc. Not sure if that would work as it all depends on the judge.
I think his reason for his appearance has to do to his charge of obstruction against the jury foreman and the assistant D.A. stemming from when he was booted from the grand jury at his prior appearance and his “charge of treason” rejected by the them in a earlier hearing.