Regarding the Beach Boys being a surf music band...they weren't. They might have been in the VERY early days but certainly not beyond 1963. They sang ABOUT surfing certainly but those songs don't fall under the surf music banner. They adeqately covered 'Let's Go Trippin' and 'Miserlou' and even attempted to write some of their own surf instrumentals - but with little success. 'Mr Moto' was an early concert staple. Largely, however, surf music belonged to such groups as Johnny & The Hurricanes, not to mention the brilliant Dick Dale & the Deltones.
Reference: 'Understanding The Beach Boys for the best in Surf Music' by Stephen J McParland.