There are two separate parts to vehicle insurance: Liabilities coverages, and the Comprehensive & Collision coverages.
The value of the vehicle should not really affect the liabilities portion, only the C&C. That is more related to where you are, who you are, and what the risk category you and your vehicle qualify as. So there is no reason for the cost of your insurance to double because the bike's value doubles. Yes, it should go up some, but not by double, or else they are just screwing you over.
In the case of Progressive, they have misclassified the 2014 FJR somehow (maybe considering it a "sport" bike now) as compared to prior year versions of the same machine, and they radically increased the cost of liabilities coverage. I pointed this out to them, just before I left them (after 10 years) and switched to Allstate, when it landed on deaf ears.