just about no one uses notwithstanding so I suggest you do the same. nethertheless, is used in an argument which allows you to put your competitor's point to one side (not reject, merely delay it, though of course the idea may be forgotten in the mean time) while you continue your own chain of argument.

I agree with Bill. 'Notwithstanding' is so rare that you may as well forget about it. Just use 'nevertheless'.