Others with more experience feel free to chime in, but I'd negotiate.
They've spent a year vetting your work and offered to hire you back. This means they like you, your work is competent enough, and they've already spent time and money training you to become this competent. In short, they're unlikely to walk away at the first sight of negotiation.
You've already found out they're offering you bottom of the ladder pay (though be careful with wide averages and practice types), so you're not being unreasonable with asking for more.
Last, negotiation can help bring out certain benefits you'd enjoy in lieu of extra pay, that would be cheaper for the employer. For example, maybe some commission from work you bring in, or insurance benefits, gas expenses (they can write those off as a business expense), etc. So don't be afraid to get creative (within reason).
Years ago, I wrote the LSAT in September of my third year of undergrad. It was fine. I didn't have to worry about it anytime close to when I was applying. The LSAT should be written as early as possible as long as you are well-prepared and have been consistently scoring well on the practice tests. Too many people leave it til the last minute and that's a mistake. You should have a competitive valid score in hand prior to applying so you know where you are a competitive candidate.