I wonder if it would help to remember that etymologically "eleven" comes from "one left" (as in, I counted the first ten and there was still one more) and "twelve" comes from "two left".

As for the others, I think remembering these in several different ways is stickiest. For example, you might think of 7·7 = (5 + 2)² = 25 + 2·10 + 4 or perhaps 7·7 = (6 + 1)² = 36 + 2·6 + 1 or 7·7 = 7·(10 − 3) = 70 − 21. If you already know 7·7, then 6·8 = (7 − 1)(7 + 1) = 49 − 1. You can try computing 7·8 by repeatedly doubling: 7, 14, 28, 56. Etc.