I wonder if you would get a good fabric still if you went up one needle size? You would still need to do some of the other things you are thinking of, the length issues. You might do a swatch with the larger needles and see if the size around for the cuff would calculate out big enough for your son as compared with the one you made for yourself.
You might also (or instead of changing needle size) add a few stitches. Here is a site that talks about heels with different numbers of stitches that might help. LINK
If you have a little experience with socks and the pattern is fairly basic maybe you could add stitches and still figure it out. Keep track of what you did on sock one so you can do sock two the same.