Ok, I can kind of follow this, but I would consider sewing the cut end. Another thought is that you could add tops to cheap soccer socks by getting two pair, and cutting the leg part off one pair, then attaching them to the others, or using the leg parts as cuff tops tucked into the tops. Maybe even using a worn out pair for the cuff parts on a good pair.

I think there is a special way to sew stretchy socks, though; stretching them a little as you sew or something like that.
Good luck.