You are in Canada, so yes, your insurance is regulated by Prov. authorities. but is similar across the country.
The problem you are having with valuation is the same as my experience since I built 31 yrs. ago. They base everything on what the cost is to rebuild 'new'. I built most of my house, so my cost of construction was low so I had to fight this forever. Didn't matter, I lost. If you insure it too low, they will base any claim on co-insured values. So if your house is worth 200,000 but you insure it for 100,000 and have a $10,000 claim, you will get 50% of your claim because you are insuring 50% of the value of the house. You must have the insurance at 80% or higher to avoid this. I had one claim 2 years ago when 2 tornadoes went through our place. Hundreds of properties damaged in our area. Zero damage to the house but it brought down our hydro pole & line. A week later and $6,000. and we were hooked up again. So I got $5,000. payout (deductible) but paid in the range of $40,000 in insurance premiums over 31 years. SUCKS.
I don't know the definition of 'primary'. I know from my own inquiries and those Cdns who post here that there is some flexibility. The other posters have it correct IMHO, they want to see a reliable source of heat other than wood. You are best to call various agents in your area like I posted and ask questions. I'm sure there must be other stoves in your area and the local agents will know best. I would NOT use an on-line company for this as I know for sure most of them I have contacted will say NO to any variation of normal. Been there, got 'no' multiple times. Ask neighbours who have wood stoves.
As far as other questions, all I can add is that my agent called me when I filled out the insurance form that requested full info on the stove. I had listed 2 2/3 cords per years and he thought that was excessive. I discussed it with him and he put it through and I have not heard back - yet anyway. The WETT info can be accessed on their web site and I had a long not so nice discussion with the head office on their requirements. I wanted to put in a Woodstock stove that was UL approved but not ULC. Can't be done unless you use the 'generic' code requirements which are absurd for a very good, new stove. There is no way to win. You are fighting the guys that have all the tools.
Bottom line with insurance is that you cannot lie. You can easily state that your 'normal' use of wood is different from last season, which was particularly cold. That is not a lie, just a 'variation of seasonal thruths'.
EDIT. I know about the insurance on WETT inspectors because I knew one really good home inspector that I called to do my stove. He stopped doing WETT inspections due to the crazy high insurance costs he had to pay. Wasn't making any profit. He explained the situation to me. Sad, because he knew his stuff and many inspectors do not.