You started out with:
"After market start button, fresh battery.
Slow crank with the button. Fast as hell when i jump solenoid.
Button or solenoid?"
Which would be, almost unquestionably, a failing solenoid. Spinning fast with the posts jumpered says your battery and the starter cabling is OK. Some problem in the wiring harness leaving very low voltage at the solenoid wires might result in a poor, and arcing, contact inside the solenoid and slow cranking. Corroded and burned contacts would do the same with proper voltage.
Now you say the solenoid doesn't even work when you connect battery "+" to one of the two control wires and battery "-" to the other. That's now a failed solenoid.
The story has gotten rather complicated now though, so I'm not sure you did that test.
Don't waste time rewiring the start button if 12V battery voltage across the solenoid wires does not result in a strong click from it - polarity does not matter. Until you have a solenoid that works reliably, testing the button wiring will be near impossible. I would disconnect the starter motor cable from the solenoid post so the starter doesn't run - when doing tests or wiring the button so it works, there's no need to drain the battery that way.
The original problem was probably a gummed up solenoid mechanism and/or corroded solenoid contacts. Properly servicing the thing may bring it back to life: used ones can be good after servicing, usable new replacements can be found at any lawn machinery shop, and new OEM ones are available (crazy expensive compared to a John Deere one though).
Once you have a working solenoid, proceed to wiring the switch.