Check out Case Western…at 1400ish score should put her in the range, and they have great programs.
As for silly mistakes, in the math section, I made myself justify every single question I put down and avoided most errors on test day.
Make sure that on test day, she reads a book (10-20 pages) in the morning before driving to the center. This will ensure that the first thing she thinks about/reads isn’t an SAT English Passage.
Best of Luck!