I would be even more concerned to find out what is causing that streak. If this is a crop from even larger image, I would suspect there is some dust on the sensor or inside the lens.
However, I also did some experimenting on editor (Gimp in my case), and I would say you should try to increase the area of selection used with the healing tool. Try diameter same as the whole streak. You will loose some nice details but the result is still good enough, I think.
Healing tool also has different settings (at least it has on Gimp). I do recommend experimenting with them to get for example "lighter" effect.
EDIT: To make this suggestion more useful, I add also here the requested example. On this quick example I used only the basic heal tool settings. The idea and suggestion that I think works adequately in this case is to choose source area large enough for the heal tool. On this example image the source area I chose, is the circle on top right, and target is the circle on lower left. Also keep in mind that the audience does not know how the original looked.