When to Negotiate Scholarship?

[glsamo]

I was accepted to and received two scholarship offers from two very different schools before getting offered a scholarship to my top choice. The first acceptance was from an "easy in" school in which they offered $27,000 per year, which pays 85% of the tuition. The second acceptance was from a semi-reach school in which they offered $30,000 per year, which pays between 61 and 66% of the tuition, depending on the data collected. I received a letter today from my top choice, which is settled in between the first two schools as far as ranking. They offered only $8,000 per year; however, this pays 64% of the tuition. I want to negotiate my top choice's scholarship offer, but I have some concerns.

First, is it too early to turn around and negotiate as soon as they send an offer? If so, how long should I wait? And what is the very latest I should be negotiating?

Second, based on the fact that their overall tuition is extremely cheap, am I thinking too optimistically that I'll be able to negotiate even though the other schools are paying either a similar percentage or more as it's still cheaper to go to this school versus the others in terms of the total amount I'll have to pay out of pocket after three years?

Third, I'm retaking the LSAT in February due to the fact that I'm not personally happy with my current score. If I do improve, can this be used to give me any leverage in terms of negotiating? Or is a February LSAT score far too late in the game to help?

Thanks!