Coal buildup is not a problem unique to bk. Any stove will do this when you are trying to produce more heat than your stove is capable of.
Huh.
Jeff in Maine, your dilemma reminds me of our curve with the Napoleon pellet stove in the house in town. The Napoleon NPS40 pellet stove is rated to heat up to 2000 sq. ft. When it was installed the guys from the stove shop looked at our house, looked at our stove, laughed and said, "This stove is going to run you out of here." Our house is a one level bungalow, 1420 sq. ft., brick and block construction with mostly plaster interior walls, no insulation in the exterior walls, circular floor plan with an L-shaped hallway in the middle of the house.
The stove could not keep up- the heat drop off just from one end of this little house to the other was remarkable.
People on the pellet section of this forum worked with me to sort out this problem. What it came down to with us was lack of insulation in this house. We addressed that issue and now the pellet stove carries the house by itself on all but the coldest days. If it is in the lower 20s or below, particularly if it's cloudy/overcast with no solar gain, or if it never gets above freezing for several days, or if nighttime temps are in the teens or single digits, the gas furnace kicks in to help, but not nearly as often as it would have before.
Our existing attic insulation was fine- dry, in good shape and installed properly- but there was not enough of it. IIRC it was R19 batting insulation between the joists, over top of the original rock wool. We left all of that in place, and Hubs rolled R-30 over top of all of it except for the relatively narrow floored portion of the attic, which we use as storage. We also had a company install a radiant barrier in the attic, on the underside of the roof and on the gable walls. We considered installing the radiant barrier ourselves but this company offered a proprietary product that breathes, as opposed to the Reflectix we found at the local big box home improvement store.
Now that we've had the radiant barrier installed, and the additional insulation, the central air conditioner is keeping up better as well.
We can't really do anything (practical) about the lack of insulation in the walls, it is what it is (the anchoring construction of brick and block limits the ability to blow insulation into the gap.) So we worked on air sealing with caulk, foam, and inserts for electrical outlet and switch face plates. It all added up to a solution for us.
Oh, and our windows were already pretty new, previous owners replaced all the original windows with double pane windows, so that wasn't part of our issue. And the insulation under the floor in the crawl space is appropriate.
Maine is much much colder than Virginia so perhaps our experience doesn't translate. Maybe you do need a bigger stove- but the Princess is a pretty big stove herself. Would air sealing and insulation help?
Just a thought.