I find myself in the same boat at times too, less than 2 weeks into school, though my time constraints aren't quite what yours are. I've decided I will do what I need to learn the law and how to apply it, even if the approach isn't all I'd like it to be.
I wouldn't bother going back and doing written briefs on cases you have already covered in class. I would (though maybe I shouldn't) assume your class notes on the days the cases were covered have the important aspects of what the professor wanted you to take out of the cases. Or just go back and do a quick read through again of them and book brief them to get down what you need to have in your outline. Remember, the brief is only a tool for you to use to learn aspects of the law and how it is applied or how it evolved. What's imporant is what you learn and take from the cases and get into the outline you study from, not having a stack of neatly typed briefs.
Are you using any outside supplements? Commercial Outlines? Example and Explanations? These are good sources as well for info for your outline. I review them before reading the cases, it makes it much easier to see where the law is in the case.
Can you volunteer to do case briefs in your classes? Or is it all cold calling by the prof? If you can volunteer, do so when you are prepared and you will be less likely to be called on when the prep isn't all you'ld like it to be. And try book briefing a few cases that aren't too long or where the case is laid out in an easy to follow manner.
Keep at it. You have a three day weekend to catch up!