I've had integration problems, as well as hate the fact that powered sub levels constantly need to be adjusted based on the source material, or the source. Possibly it is me, or the subs I've used, but have just never found happiness.
Decided a number of years ago that I would no longer use a sub for 2-channel (HT only), and that I'd only buy bass-capable speakers. No regrets, especially as the quality of the bass is so much more natural and tonally correct when it comes from the same speaker where the high stuff comes from.
I'd likely change speakers. However, if you love your BAs, then as others have suggested, a pair of passive subs is all I'd add; one underneath each speaker.