Ya, it's just a matter of time. If there's a way of speeding it up significantly, I can't find it. I mean, the sauna will speed the evaporation part up a bit, but if evaporation is only getting rid of .5% of the alcohol in your blood, even doubling it isn't going to make a perceptable difference.
I used to hang out with a guy who did research on the subject (basically got people drunk and did various experiments), and he said much the same thing.
Sorry, I meant to have paragraphs in there, but something happened to my line breaks :|
Your binge drinking is causing a spike of acetaldehyde in your blood, which is more toxic than ethanol and generally makes you feel like shit. It also makes beer taste like green apples, but that's a different story.
Since you're drinking so much, you're loading your blood with a level of alcohol and (consequently) acetaldehyde. Your blood has enzymes to get rid of these things, but only a certain amount. So, while normally the level of stuff in your blood drops at an exponential rate, like this-
when you drink too much, you clear it at the same rate that you create the necessary enzymes, so your level decreases linearly, like this:
(the labels aren't important, just note the shape of the two graphs).
Basically it just means you feel like shit longer when you have too much to drink.
wikipedia has a good article on hangovers, you can check that out too - Clicky