Clamp a straightedge down across the body right up next to the gouge, maybe 1/32" away from it. Take a sharp knife (a swiss army knife sharpened well is good) and make several passes gradually adding pressure to make a nice clean straight cut. It won't be deep, but it will set you up for the next step. Remove the straightedge, start at one end, take a 1" chisel and lay it in the cut with the angled side facing the gouge. Tap it with a hammer until it's as low as the gouge, then remove the waste by laying a 1/2" chisel flat side down in the gouge. For the side where it slipped as you were exiting, the lower edge of the gouge in the picture, you will need to widen the gouge as wide as the worst spot. So, after making the cut with the knife you will need to slowly work your way back, removing about 1/16" at a time until you get to the line.
Once you have nice clean straight edges to the gouge you can make a patch and use your block plane or sanding block to fit it. With the grain of that wood this should be a nearly invisible repair.
Red line is where you clamp the straight edge, make the knife cut and final chisel cut, black lines are wood that needs to be removed before getting to that line. You only want to be removing a tiny bit of wood on the final line. That way it will stay straight and the chisel won't have the tendency to push back into the wood.
Another option, and I'm not sure if it's possible without looking at the whole thing, would be to clamp a straightedge down and use your router to cut the gouge. Either way, you need to get the edges of that gouge straight and clean so a patch will fit in with no gaps.