We have a state run rehab in Maryland. People call to get in. People (I did this) call EVERYDAY and are told to do so as they want people who are truly ready to stay stopped. I don't know if this helps anything, but it tells me that the state doesn't want to waste money on people who aren't absolutely serious.
If you are serious, slow your drinking and before you know it, your 3 weeks will be here.
Alcoholics want what they want when they want it. It's a form of control.
Keep searching, if you want, or accept that your help will come.
Just my experience and suggestion.