Sorry "Never give work full rights to everything you make on your own time." is not going to work there is to much precedent in US employment law.
Work for Red Hat? You own your free software contributions, even those made at work. Work for Google? They own even the small lump of green putty you found in your armpit one midsummer morning.
Many companies will apparently put in grab-all clauses but back down (but Google won't) if you call them on it.