Mr. Deshazer has spent six years incarcerated. He is awaiting trial. Can he appeal his continued confinement on speedy trial grounds prior to trial? No.
The U.S. Court of Appeals "does not have jurisdiction to review interlocutory review of orders of the district courts refusing to dismiss trials on speedy trial grounds."
Translation: The right to a speedy trial exists only in the grace of the trial court judge. You can't actually enforce it until it is a moot point, when you have been acquitted or convicted.
There is some chance that review by what is called a "writ of mandamus" can address the problem (this is a direct appeal to the top of the system). But, more often than not, there is no relief available if your rights are ignored.
This situation is actually more common than most people realize, either through absence of an effective appeal, or through broad standards and abuse of discretion review on appeal. Often, trial court judges make final, irrevocable decisions from which there is absolutely no recourse, even if the judge gets it wrong.
In the case of the right to a speedy trial, in this age of government abuses of process in terrorism cases (although the linked case is simply an attempted kidnapping and assult case), this is particularly troublesome. Maybe you'll get a good judge, maybe you won't.