That is interesing. A 10" 870 really sounds like a
Class II weapon to me, not an AOW. Where did you get your "...one time $5 tax (Permit)..."?
Also, keep in mind that, even with a Fed "permit," individual states (such as CA), can prohibit your possession of lots of weapons
(link) "...These weapons may also be further regulated by states or
localities, and while these weapons can be legally owned under
federal law, some states and localities further regulate ownership
or prohibit it (see below)..."