Purely anecdotal and IANAL, but I was under the impression that companies were only allowed to confirm or deny your employment, and not give feedback about your performance. Is this a state-to-state issue?
Most places I've applied to have asked for references separately from the initial application, although there will occasionally be one that asks for previous supervisor names on an application. I've seen some that had checkboxes to indicate if the company was allowed to contact the person or not.
Have you given written notice of resignation? I've known of some people who provide one to act as official proof of your resignation, and you can indicate things such as giving them three weeks notice.
Anyway, you're probably better off just sticking to the three weeks you've already said you've given them. If you've already told your future employer your start date, you don't want to start off on the wrong foot and upset the new bosses. And some companies will try to pile work on anyone who says they are leaving. Sometimes it's valuable work, but other times it will be a form of punishment. Sad, but true.
I hate to say it, but if you don't finish something, what are they really going to do to you? I know a lot of people have a sense of professional conduct, and I've personally stayed late at jobs on my last day to finish some stuff off, but if they are going to be blatant jerks, I don't really think you owe them anything.
As long as you're not screwing anyone over too harshly, I don't think there's a problem with you leaving when you originally planned. From the sounds of it, it's not a very nice place to work, so you're probably better off leaving as soon as you can and getting a fresh start. Hopefully your new place of employment will be nice. You never know until you actually start working there (speaking from experience).
Oh, and I'd be curious if HR had an exit interview planned with you. This is something you could bring up there or contact HR prior to leaving, in writing. This decision probably plans on how objective your HR department is. No harm in not wanting to rock the boat, but I don't think you can let your previous employer push you around like that.