Per the question, I used Minwax until it faded, but it was still quite obvious and visible (close to the last pic in the question post).
Then, taking a page from the "mayo and ashes" tip, I mixed 1-part mayonnaise (Hellman's) to 1-part baking soda (not baking powder; I used Arm & Hammer brand) as a cigarette ashes replacement. I rubbed the mixture along the grain directions using a paper towel and some pressure.
The stain faded, then vanished. The resulting wood is smooth, and considering the baking soda is abrasive, appears unscratched. After wiping off the mayo mix, my table may smell like a turkey sandwich, but it's beautiful again.
Now all I have to do is polish off all the Minwax buildup from my earlier cleaning attempts.
I would never have thought of going with the grain had I not spoken to the lady from Restore and Adore, and had the baking soda idea fell through, I would have gone with the "last resort" 4 0 steel wool with a lot of Minwax applied.
Pic of the repair:
![repaired table](https://i.stack.imgur.com/J1dBB.jpg)
If the wood is dented rather than cut/gouged, you can steam dents out with a clothes iron (preferably a steam iron, but not required if you keep the washcloth damp), a damp washcloth, and some patience.
If it's actually cherry, and not just "whatever, with stain, called cherry since we used a reddish brown stain" it is best to remove and not replace the stain. It will start rather light, but age beautifully with time. But that is a matter of opinion. Your best bet with re-staining it is to take the whole thing back to wood, and re-stain the whole thing if you are going to do that - then it will all match. However, some slight mismatch between the top and the rest of the piece will not be as glaring as a mismatch between two halves of the same part. Try to find some similar scrap and test your finish process and colors on that.
Best Answer
BLO is a good stand-alone finish for things that won't get wet. That is to say that many people like the way it looks on it's own...but it does not provide any significant protection against moisture.
For instance, it would be terrible as a stand-alone finish for an eating table or a side table in a TV watching area.
Very nice though for something like a TV stand, or a rocking chair or a picture frame.
Be sure to read up about fires from drying BLO rags. BLO is unique in its ability to create enough heat while "curing" to light itself on fire. Many garage fires have been started in this way. As long as you handle the used rags properly, no problems. Just tossing it into a trash can in your shop along with wood and sawdust...not so good.