Nearly there! Quite a challenge, very enjoyable.
I can't see the two groups of letters at all. Reading the comments here, it seems they form words. I'm near certain about what I should shade, but can't make sense of those two groups.
And can't parse 10a - is it just a double definition? If so, don't get the first one.
Incidentally, I am firmly in the 32 cells camp (assuming I've understood correctly at this point). The preamble is careful to distinguish between letters (two groups of them) and cells (one set of which is to be shaded). So the corners can be part of the set of cells, without the letters therein being part of the group. Plus, not shading the corners would be lunacy.