Hi Steve! Great Question! Much will factor into a solution ...
Do you have "professional status"? I am a business owner and deal insurance needs trough my Professional Organization. Sometimes AMA will want to bring people in with membership incentives. Monnex will quote "preferred rates" with association to a College (NAIT) or University (UofA). Even excellent credit card status can get you in on so- called "preferred rates" as Insurers like Monnex might if you are tied to TD Bank in any way.
Unfortunately what "we" in Alberta currently have going against us is the Ft. Mac Fire and the Calgary Flood along with other recent "weather" events. These have hit many insurers hard and we are seeing the continual increases for it. So I hope you have an association access of some sort to a preferred rate. The other thing insurers like to know is how my KMs you put on it each year ... keep it as low as possible and with truth as they don't like finding out you drove more after the fact ...
With Corvette Insurance, I found that my 2016 Stingray has inexpensive rates when compared to earlier Corvette models. It sure has a lot to do with driving record as well. Multi-vehicle discount rates are also advantageous as the Corvette would avoid being the "primary" endorsement (most costly). Keep any graduated-license drivers off the Corvette if you can (if applicable). Tie-in home insurance with the same Company and save as well. Add Annual Out-of-Province Travel Insurance. Look into a Tie-in with Business Insurance (if you have a Business). Its good to check for the potential to reduce the cost of everything together.
So, answering your question, I have year-round insurance that can be put "in park" depending where it is parked. If it is 100% in your control and on your property then fire and theft is all you need. If parked anywhere else, you would have to consider liability in the event that some dumb-a$$ hurts themselves near your vehicle .
I have insurance on my 2016 Stingray and two 2015 GMCs that is only reduced by $40 per year when I put the Corvette in park, my annual premium is very inexpensive for the Stingray, so I keep it fully insured year round for a cost with only three numbers $XXX.00 (I am fortunate compared to some on a year round price). Talk to your agent about doing the cancelling thing as it will often work against you for renewal rates. For those reading this with a new Corvette and are considering the "no loss depreciation" you never want to cancel the policy as that option might go away as you can only get it with most insurers in the purchase year and then it perpetuates for year #2, #3, etc. I have it on all 3 on my vehicles! (I have experienced a write-off with no-loss and got a new vehicle - what an investment that was)
I (as likely with many others) am interested in knowing how this works out for you as I diligently compare insurers and options every year on renewal dates.
Cheers!