Yeah, that Jackie & The Cedrics clip is a modern classic!
Sorry for my relatively long list above. If I had to pick just 5 bands, I would probably go with The New Dimensions, The Astronauts, The Super Stocks, The Surfaris, and Jan & Dean.
And in addition to my original list which is mainly made up of bands that released at least one album, one should also not forget that there were loads of bitchen 1st wave surf groups that only put out a 45 or two on small labels.