Unfortunately, I think the U.S. may have laws that complicate this issue. For example, I believe laws make sure the test is administered for free by health insu

Unfortunately, I think the U.S. may have laws that complicate this issue. For example, I believe laws make sure the test is administered for free by health insurance and I think there is precedent from the Americans Disabilities Act that employers pay for any testing for those employees do not have insurance. While I think your idea of a nudge may work, it may not be feasible in the U.S.