I may be quite late to the party, but another way to "fix" the problem would be to blend the beer. You could just brew up another California Common using the same grain bill and underhop it -- put nothing or only a tiny bit at 60 min, and then heavily late-hop it for a ton of flavor and aroma, making sure that the bitterness is still far below what you'd want in a California Common. Then blend the two beers; if you did it right, you might end up with something that not only has the right bitterness, but also is brimming with the aroma and flavor you want.
(I've done this before, to fix over-spicing, rather than over-hopping, as well as just to blend two beers together that go well; in fact, I've also used a very dull beer to bring up the ABV on a flavorful but thin beer. Blending can be a great way to fix problems. I'll admit, it's not guaranteed you'll get two beers that will mix well, but chances are much better if you're using the same grain bill and the same hops.)
And it is possible to get the beer very flavorful hopping heavily but only in the last 15 minutes... but from the results of an experiment my brewclub did a while back, you'll probably want to dry hop anyway. (For some reason, hopping beers exclusively in the last 15 minutes seemed to make the aroma less powerful than we'd thought. No idea why.)
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