You could fill the gouge with uv cure resin, like suncure or something. It's got milled fibers in it, usually, so it's thick. You can shape it, then hit i with sun to cure it. Or give it a flash of sun, then shape it, then give it more sun to fully cure it. Use a smooth, clear plastic bag to conform it around curves, hold it over while curing. It's easy. Clean/prepare and lightly sand areas you want the resin to stick to.
Redoing the finish would be annoying if you asked me. You'd need to get to bare wood, then mix up and brush on some resin.