I see the point, and I get the sense if my answer isn't to your liking there is a 2nd Amendment tirade in the shadows.  

Proposal only:  Certification could be done by private schools.  And yes, they have to keep records, but not in a unified government way.  There would probably need to be oversight that the schools are providing the needed info and not just sending bodies through a turnstile. 

By reciprocity you mean one state recognizing another's laws? Have to admit I haven't thought about it much, and not sure I have a clear position (as it wasn't central to my statement above).  That is an interesting one.  I guess my first reaction is States have rights to pass laws for their area.  Perhaps the analogy that might apply would be if CA passed a Transgender Bathroom bill, would that entitle a Transgender person with CA residence to walk into any bathroom in Texas or Carolina just because they could back home?