As the other poster said, you are hardly alone with the convictions, and they are far enough in the past that as long, as you disclose and are cool with the bar, they probably won't be a huge deal (from what I've heard).
I'm feeling you on the GPA. I was ill for a couple of semesters in UG a million years ago, and did not withdraw from the courses I dropped bc they did not appear as Fs on my transcripts and the grad schools I was applying to did not care. Drops my 3.85 down to a low B and really limits my options.
Best advice is to nail the LSAT. A few points can make a huge difference.