I would do it like this: since the Red channel shows the black lines, make a duplicate channel of it, and use Image > Adjustments > Levels to clean it up. Do the same for either the Green or Blue channels, for the white areas.
With this document still open, File > New, and from Document Type, choose your original doc from the list (near the bottom), and transparent contents. In this doc, Select > Load Selection, with Source Document set to your original doc, and the Channel to the copy of the red channel, with the invert box checked. Fill this selection with White.
Similar for the other saved channel, only the invert un-checked. and fill with black. Save this as a .PNG, and you should be good to go.
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