IMO, the easiest fix is to fill the gouge, then with great patience, try to disguise the area with tiny brush strokes of black to blend it in. IMO, you are fortunate that the damaged area is replete with black streaks. They will make the repair much easier to "hide".
If I were to try it, at this stage in my learning, I would use acraglass, and stain it to as close as the base wood color as possible. Then, add the black streaks with the tiny, hobby paint brushes. i think that the "judgement seat" will be how well you match the base color.
Go for it. Projects like this sometimes end up much better than you expect them to.