damaged crotch walnut top

Having refinished for 12 years professionally, I never had total luck with fill-ins at a high-bar level, especially on things like tabletops where all the world can see everything. And you’ve got something 2 inches long and over 30 thousandths deep.
That being said, sometimes you do catch a break and your touch-up, filling crayon, whatever, works magically and you move on.
I would try to fill it with brushing lacquer first, then let it sit for a long time, maybe even three-four weeks. Then I would go back and start leveling it with fine paper attached to a perfect flat board. The trick is to level the brushed on lacquer, without knocking down the original finish. Small board is better here.
Once level, you can start using polishes and products like Novus 3, then 2 to achieve a smooth finish. The satin is a blessing and a curse. It’s somewhat matted, so you are not trying for a mirror finish. But you are going to try and recreate the gloss level of the original lacquer, which is low. Hard to hit that particular satin matte so it all looks the same. Actually harder than recreating a mirror gloss finish.
What’s the worst that can happen? You end up stripping it…

-- Paul, Tennessee, http://www.tsunamiguitars.com

I have nothing to add to Paul’s outstanding reply except that your dogs are quite handsome. Good luck! :)

-- My dad and I built a 65 chev pick up.I killed trannys in that thing for some reason-Hog

I wonder what puttting a damp towel over the area and steaming it with an iron would do? I obviously have no idea but maybe someone will chime in on that thought with more experience than myself.

-- "there aren’t many hand tools as awe-inspiring as the #8 jointer. I mean, it just reeks of cast iron heft and hubris" - Smitty