What do people with Rumford type fireplaces do? What do historical sites with, say, wood fired ovens do? What do commercial sites using various high temp applications so (read restaurants, pottery studios, etc.).
Here's a few things I've found about insurance companies, though note: I'm not in the biz - just had to deal after a fire in my parent's home.
Sometimes insurance companies take into account (or require) stuff like 1) Fire alarms connected to a service agency which calls in the FD if they get a signal and don't get a "cancel" from you w/in 3 minutes. 2) Fire sprinklers installed. In all or part of the house; rules vary. 3) Type of building, type of construction of the building. 4) Number of people using the building. 5) Type of construction in/around the room with the suspect appliance (2-hour firewalls and doors, stuff like that). 6) The type of room in which the appliance is installed. 7) Number of floors of habitable living space; floor level of the appliance.

The material used for the appliance itself. Some materials are less offensive to insurance companies than others.
Just some variables to run by agents when seeking out options. It's usually necessary to have required work done by licensed contractors and inspected by the the
local AHJ (Authority Having Jurisdiction).
Shop around... A lot. The policies are quite intricate and difficult to puzzle out and they can vary considerably. You really want to find a cooperative agent or three who will take the trouble to understand your issues in detail and then take the trouble to put together a path through their official maze of requirements. I believe often there is such a path, but it takes somebody familiar with the "rules" to and willing put it together. Companies often have very specific keys which they use to flag or pass particular issues but just as often have generic rules which will meet their requirements. The major one being the previous para, having a
project done "officially" and professionally. They need to see things in terms they understand, such as "wood burning fireplace, brick construction, stainless steel flue, professionally installed per local codes, permanently installed in room of non-combustible construction with two ADA Compliant Egress Paths". Stuff like that. But you do need to clearly disclose the correct name of the unit because otherwise any claims you might have to make later could be disallowed (regardless of whether they had anything at all to do with fire). Note, though, that there are often several correct names and some may be much better for your purposes than others.
Often it boils down to a people thing. Search for the right people who know their business and can and will make the effort for you. In this case, the guy 30+ years in the business is a better bet than the young and eager fellow no matter how compatible he might be. But attitude counts, of
course. <g>
Best luck.
Rufus