Wow, you really caught a lot of that piece. I think you're done except for cropping, sizing, and printing. I'll take a couple prints. Definitely one of  number 5 of the Dinolite pics. 8 x 10 will be fine. 

Pretty piece. I believe that cell structure is Conifer.
With all those fractures it would be very tricky to polish. You can't tumble it so you would have to do it by hand on a flat lap or cab machine. With the coarse grit you would start with to get the saw marks out you will find out real quick how much is going to stay together on a flat lap, so I'm thinking easy as you go on a cab machine.
The second of your first two pics is probably the best side. The darker square covering bottom right corner looks the safest. No telling if 'all' of that lighter 'border' will stay attached.
I like the pictures. I know those saw marks are bothersome but you will probably sacrifice 'some' of the piece in the process of polishing.
And BTW, if you use Baby oil in the future, lie and call it Mineral Oil. HA, Sounds more professional.

The other thing to think about is how much of what you can get in your photos will you be able to see and appreciate in the polished surface/

Had to recharge the battery for my camera, which meant finding the charger..  Finally found it this morning, battery recharged, so here's the side pics. The fracture area in question on pic 1 is the top of pic 15 (last pic). Looks pretty stable to me, but I could be wrong. 

Well, whatever it is, it's on the surface & looks metallic. My Dino-lite (like most of them) has a built in polarizer for the LEDs, so I used it to show what I mean. 1st pic is fully polarized, the 2nd at 75% polarization & the 3rd is non polarized. Looks like metallic smears & dots, in line with the saw marks.

*looks up the address for Dr. Joe's Rockin Clinic* 
Not really wanting to test the tumbling prognosis though, I would rather keep the sides rough & natural looking.

Scott LaBorde wrote on Oct 27^th, 2021 at 10:39am:

Actually, Joe has it right now, grinding the snot out of it (because nobody wants snotty pet wood). And since he might charge an arm & a leg, I have to find suitable ones to send him.. I sort of need mine.  Saw grooves on one side are getting leveled.