I've never heard of storage rates, but my 2 vintage rides are with State Farm classic car coverage and they won't let me suspend all but comprehensive in the winter. The rates are low enough I don't lose much sleep over it.
For my '09 Challenger, I call them after thanksgiving when I put the car in hibernation, and cancel all but comprehensive coverage, then sometime in March when I am ready to drive the car again, I call and resume all coverage. I don't have a loan on the car, if I did, I would have to keep full coverage at all times as that is a bank requirement. Having title in hand saves me more than just loan interest!