I used to use spaced repetition (e.g. Anki) with my coaching clients, but now I have some more targeted exercises. Using spaced repetition, consider each fact “known” if you answer it immediately. So if Anki asks you “6×8” and you’re like “oh yeah after 40 it’s 48” rather than immediately knowing it’s 48, then I’d consider that as not yet “known” for the purposes of Anki.
There are only 55 facts to learn (ignoring the 1× and 10× tables and duplicates e.g. 6×8 with 8×6) and you’ll know most of them already, so it won’t take long to drill them.
Regarding tables up to 20, I generally recommend to learn up to 19×9 but not all the way to 19×19. The former is much more useful, because you can use them for splitting up larger multiplications. For example, 57 × 17 = 850 + 119 = 969 if you know your 17-times table. You don’t have to keep the area that you learn a square 
Regarding tables up to 99×99, I agree that this takes a lot of work. I count 4005 multiplication facts (ignoring 1×, 10×, 20×, …, 90× tables and duplicates) with an average length of almost 4 digits, so about 15000 digits. Unless you want this as a specific memory challenge, I consider it very high-hanging fruit in the context of mental math.