I see the problem now... Are you going to power cost/paint the swing arm when done? I can't recall what you said you are going to do with the frame, but I've seen some really nice looking nickel/ cadmium plated frames in the past... If so, then you could make the swing arm the same and...
Fabricate something from sheet metal to wrap around or over the brake line. Formed in a shape to wrap around the line - Ω If one side was welded in place, then the other could be pushed gently down (depending on the gauge!!) over the line until almost flush. If wide enough - a small short screw could hold it is place... Length along the swing arm could be short (and more than one) or one longer one... I can visualize it, not sure it is practical, that it makes sense, or that you'd like it...
Cheers, Adrian