Slight pulling at the 8k level to me says it probably needs more time on the 8k, or failing that - a tiny bit more time on the hone below to polish up some of the deeper scratches. Then again, it may just need some stropping.

I wouldn't judge where the Barber hone is by feel alone. Hone a razor on your 8k, look at it under magnification. Then do a few strokes on your Apart and see if the edge improved. Also - I would imagine if you don't want to lap barber hones, abrasive cleaning pads are also on the do NOT use list. Circles back to removing binding material and potentially exposing too much of the cutting material. I would stick to soap, water, and paper towels if anything.