My Fireview is even more boring than your BK in "black screen" mode; the glowing cat is not visible unless you are on the floor looking up above the glass; I suppose I could lay a mirror on the floor to make it easier to see. Can you share a bit about how you burn your BK? What setting would you need to achieve some lazy flames?
A cat stove will surely help that. While my old stove was a cat stove, it was rear draft and not designed air tight so I too had rather short burn times. If one day I get a BK, I would likely run it as I am running my Fireview; flames when I want something to look at, dark screen when I have other things to do or am sleeping. Good luck with the BK search.
It cycles from da r k screen to lazy flames as the thermostatic damper does its thing. As far as a setting, can't tell ya. It all depends on OAT and barometer. As it gets colder the set number actually gets lower too (less air opening). Hope that helps. I still want to do my time lapse burn but it's been so warm that I don't want to load it up to the gills or I'll cook us out, even on a long low burn....
It would be cool to see the flare up cycles. This year, for some reason, my bk has been more boring than usual. No flame, no glow, blackened glass top to bottom, but steady glowing cat and no smoke.