That's a great idea, if only for the discounts. But I don't think we could do that in CA. You supposedly must get a CA license within ten days of arrival which I did. However, it was a long time before I registered my car here (WI kept renewing it by mail) and Farmers was willing to issue insurance then on an out of state vehicle. I will look into this, as I have un-registered to vote and the property tax exemption for being a state resident is teensy. However, I do take dirt-cheap community college classes at resident rates.
Did you surrender your Florida DL? You must do that to obtain a CA license.
Have your license "lost" and replaced. Use your "lost" license to obtain another state's license. The numbers on both licenses are the same (at least in AZ), so its completely doable (and done by several people I know, since AZ licenses dont expire until you turn 65 years old).