Sooteater does work in a BKK from the inside.

Fish the ball behind the center support at the bypass opening, wedge the head about 6" into the pipe and go to work. Only issue was the door edge marred the surface of the rods a little, not enough to be concerned about though. I used a cordless 18v drill, no issues.
I did cut the whips to 5" from the ball beacause as I suspected, the ball did ride the walls of the pipe on the 45's. Seemed to work fine.

That's good. I just use the Viper with a poly brush, it works great. I've never used a sooteater, but I hear it's a good alternative.

Viper looks good, but a little pricey for me.
I posted this because I said I would when I finally did it. I bet jeff-t will breathe a sigh of relief, knowing it will work on his sisters pipe.
I went 3-rods up from the inside, to the first hard bend. Then 5 rods down from the top to that same bend. Worked like a charm.

I really like to push the broom from one end to the other. Just to make absolutely sure the flue is clear.