Just off the top of my head - an executive order to Holder: Obey the law of the land; charge them and try them on a timely basis or kick them loose. It's the law.
"But they're bad guys, probably, anyway!!". So what? If we don't obey our own laws, so are we. I'd rather they be bad guys than me. If you have to let them go, keep them in mind and if you see them attacking us with a weapon, shoot them in self defense rather than trying to arrest them. Doesn't seem terribly complicated. If they go home and raise a ruckus about their bad treatment and cause bad feelings about us, so what? It's their right. We can tell the truth in response. That should get us out of trouble, right?

An alternate solution would be to order the cessation of quacking about "the land of the free and the home of the brave" before every frigging sports event until until we can stop ignoring the constitution to keep our brave citizens from widdling their undies in terror of terrorists (anybody who doesn't look like them.) That might do it too.

Yes, people charged with crimes should get speedy trials.

Yeah, that's the law, at least on one of our levels of law. I'm aware we have one standard of law for the ruling class and another for the ruled, but do we have a third standard for political convenience?

And people captured "on the battle field" should have speedy hearings to determine whether they are POWs or illegal enemy combatants or civilians or soldiers or whatever.

Ignoring the vacuous claim that the whole world is a battlefield, this is a very tiny fraction of them. A much larger percentage were grabbed because of vague accusations or were sold to us by warlords who had an ax to grind. If they're not active military personnel, they're criminals at worst, possibly innocent bystanders. Charge 'em or cut them loose.

Congress deliberately made it impossible to do so without its consent.

Heh... must the be politically inexpedient version of the rule of law. They won't fund transportation? Obama is still the CIC of the military. Put them on a military transport and put them back where they got them. We got them from a barbarous place where people will be mean to them if we put them back? The mean people are not under our rule(s) of law; we can't do anything about them and if we can't obey our laws, why should they obey laws they don't have? If it's such a rotten place, can we get OUR people the hell out of there?
I agree that our legislative branch are a collective bunch of corrupt shitheads and they're our fault because we elected them. They are not all powerful though. They control the purse strings and and block legislation. They can also bloviate on Fox news shows. They can't keep the president from saying "General, send a transport from local base [x] to Guantanamo, put prisoners [a1..an] on it and take them back to place(s) [x1..xn] where we got them and release them with their possessions if we kept them. Do it now." The CIC bit does work with the military. Let congress try to defund the military. That would be fun to watch.
The presidency is touted to be the most powerful position in the world. Obama is acting like he needs permission to go to the bathroom. Considering the lethargy he proceeds with and the alacrity with which he accepts refusal, I have to assume he is getting what he wants. Nobody really believes that the poor fellow is less useful than a margarine dildo.