Regarding the wood stove and getting insurance. I'm sure it depends on your location but we got insurance on our house with the stove. Did it raise a flag? Yes. But the cost of insurance for the new house which is twice the size of our old house and worth far more, was about the same as the old. We eventually went with Farm Bureau insurance and drastically cut the cost of insurance for the same coverage.
Insurance and mass. Based on the questions asked by the insurance company the one thing that helped us with the insurance and the wood stove was the finished concrete floor. Its hard for the floor to catch on fire.

Course the insurance company did not have a check box for Finished Concrete Floor so we had to use tile instead.

Since we don't have carpet, can't stand the stuff, the slab acts as a huge thermal mass. It works. The wood stove sits on a brick and granite hearth. The brick is doubled so that the hearth is seen in the master bedroom and the study so that the heat from the stove can radiate directly into those rooms. The hearth is a fair amount of mass in the house.
We went through the idea of ICFs but we could not justify the cost, we kept bumping into a cost of an extra 5% over stick construction. Plus we knew we where putting in huge area's of wndows. Why have this expensive wall that is supposed to be energy efficient but then punch 8'x6' holes into it?

We wanted the ICFs to protect the house against falling trees but in the end we went with 2x6 walls with the 1 inch foam. This got us about the same R value as ICFs and some strength but at less cost. Given the window holes maybe we should have just kept 2x4 walls but I think we made the right decision.
You can add mass to the house without having to involve the exterior walls. One of our earlier designs had a sun space that ran the length of the southern side of the house. We wanted an eight foot "room" for solar gain. The idea was to grow some plants as well has the passive solar design. The "room" would have had extra mass built into the interior wall to hold the solar heat. But that idea was just to expensive. There is a NC Solar Center at NCSU. We went there in December a few years ago after we had days of temps dropping into the teens and 20's overnight and not getting out of the 30s. The NC Solar Center house had a bunch of passive and active technique/technologies. It is bermed into a hill for instance so the first floor has roughly half the house covered by grade. The house was so hot inside we had to take off our coats and sweaters. The porch that was enclosed by glass was 90 degrees while the outside temp was in the 20/30s. The downstairs was built out of CMUs if I remember correctly. The upstairs was stick built.
The Enertia homes I mentioned in an earlier post use the 6x6s and other large diminsion lumber as thermal mass in the interior.
Later,
Dan