I am less inclined to use a wire brush with steel bristles and much prefer one with brass bristles, just so that the threads aren't damaged. Don't scratch the brush across, but follow the threads round and round.

What material is the cup you are using on the non-drive side? If it's aluminium, that might be where the shavings of metal are coming from. I've had a similar problem with an older frame; I think if they were using cup and cone BBs with loose balls (or ones in a cage), the cups were probably a little thinner in width, so they didn't run into interference with the seat stay protrusion.

I suppose you could keep turning with a BB tool as suggested, or take it to an LBS for chasing, but that isn't going to fix the BB protrusion without some additional effort with something like a Dremel. I could suggest that you file down the new supporting cup so its reduced width would fit. If the cup is aluminium or plastic, that wouldn't be too much of a chore, but steel might be a pain.

Nice colour, by the way. What brand, year and model?