To Appraise Or Not To Appraise

[CarRacer]

I own a Galant VR4 and am a member of galantvr4.org.
A few members have posted having accidents and their related problems dealing with insurance agents.
The insurance wants to give them 1500-2000 dollars and the cars are worth more than that. A few have done their homework and have gotten checks for what their cars are worth after doing quite a bit of legwork and using a lot of time.

I would obviously like to avoid all of that hassle. I was thinking of having my car appraised when I get it ready for the road.
My worry is that after the value is roughly double what a "regular" galant is, my rates will go up. I figure the insurance company will justify that they are insuring a more valuable car.

How should I go about it? Play dumb and insure a base model Galant, or appraise and risk higher rates but less hassle?

Thanks