Don't give up hope! I think you're in decent shape...
I'm curious what your overall LSDAS GPA will look like; from the sound of it, you had three years at 4.0 and one (?) year of crap grades, so you're at least a 3.0, likely (a little) better, right? So that's something.
If LSN is to be believed, people with 3.0s are getting into your target schools with 150-160 or less... granted, the LSN sample size for those schools is incredibly small. The LSAC calculator
concurs, though: a 3.0/155 candidate is quite likely to get in.
Now it's possible that you didn't say, or I misinterpreted, something that would change that. If your GPA is much less than 3.0, or if "academic probation" means dishonesty as opposed to flunking out, then you might have issues -- but, with those target schools, I think you're in good shape.
That said, a couple thoughts:
--What do you mean "public interest"? Are you talking about criminal defense or prosecution type stuff, or like "I want to work for the ACLU"? The latter type of job would be pretty competitive, on par with major firms. Don't assume public interest = easy to get.
--You seem awfully self-defeating w/r/t the LSAT. I feel like (in my experience) a lot of people are so ready to say "I don't test well" that they end up blowing off prep, having lots of anxiety, and --gasp!-- fail to do well. Now, it looks like you're not going to need to ace the thing to reach your goals, but I really urge you to take as positive an attitude as possible, for two reasons: First, if you go in thinking your cap is a 160, you probably end up in the low 150s, and while that might be enough, why add risk? Second, the better you do, the more likely it is that you will get scholarships, which means you can take home a lot more of your (likely meager) public interest paycheck. A few more correct multiple choice questions on one exam could mean thousands of dollars... not the best system, perhaps, but the one we've got, so make it work for you.