That is a tough area even if you completely strip the frame of all paint. The paint and rust sticks to the area inside and at the junction of the Braze on and the tube. I have several hobbies of which one provides me with brass brushes for different caliber tubes. I think I have been using a 22 Caliber brass brush.

Although I haven't tried it, you could put a "dam" around each using a putty of some sort, like plumbers putty and fill with OA. Now that I have verbalized it, I may try it myself! My experience is that OA will not remove or discolor paint.
[IMG]P1000852 on Flickr[/IMG]