As one who's been accused of being a BK fanboy, this one may surprise some folks, but I wonder if that's the best choice for a house with this much daytime solar gain.
I have two BK's, and one is in a wing of the house with a lot of solar gain. Not an engineered passive house by any means, it's just a newer 1990's addition with 6" framed walls and blown-in cellulose, with a crap-ton of windows. I find that I need to watch the cloud cover forecast as much as the temperature, in choosing how I load it, as it can be easy to overheat the space on even a cold but sunny day.
I load this stove most evenings, and simply check the next day's forecast. If it's cold and cloudy, I load it full, and set the thermostat for a predictable 24-hour burn. But if the forecast is showing full sun, I might just do a half load using the same thermostat setting, aiming to have the load burned thru in about 12 hours. If this were my primary stove, rather than just a secondary stove heating a smaller area, I'd probably be more scientific or careful about it.
For you, esp. if this will be your only stove, you'll quickly learn how much to compensate the outside temperature for "partly cloudy" vs. "partly sunny", and load accordingly. But if your clime has more sunny than cloudy days, you may find yourself not often taking advantage of the super-long burn times possible with a BK King, and more often short-loading it for quick overnight fires only.
As to heating a 6000 ft2 home with a stove, we can all sit here and debate it, but it's useless talk without knowing the layout and dynamics of your house. Your indication of passive temperature delta (30°F!) makes me think you don't need a whole lot of BTU's, despite it being a larger home, but you could easily run those basic numbers. As to distribution, stoves put out much lower BTU than your central heating, but over a longer time. This aids in keeping things leveled better than you'd expect, if used to basing your expectations on a higher-BTU intermittent heat source. That said, there's no harm in using your stove to provide some base load, while allowing multi-zone central heating to modulate final comfort atop that, which is essentially what I'm doing in a home of similar size to yours (6700 sq.ft.).