1965 Starter spins

I'm starting a new thread because I had asked a question in Pronkie's post (thinking he had fixed his problem) but since his is still ongoing, I didn't want to keep taking away from his troubleshooting.

I have an issue where when my car is cold the starter seems to engage just fine, or at least fine for the first attempt.

Then if I drive her around for a bit and turn the engine off, the starter will turn the engine just enough for the first piston to fire and then the starter goes into spinning mode without the engine running. It is like at the first sign of hp from the engine the starter disengages. Which I'm sure it by design, but not quite that early.

I am usually ok if I give it just a little gas while trying to start the warm engine and then it revs way up once it kicks, scaring anyone around with the loud dual exhaust. If it doesn't go though right out of the gate when it is warm, I could be there for 10-15 twists of the key before it actually engages with the flywheel.

I hate spinning starters. It is very embarrassing to have a nice old car and be sitting in front of a busy resturaunt trying and trying and trying to start it...

So I am wondering what is my first attempt at troubleshooting this issue?

Thanks.

.....and don't say "Stop parking in front of busy resturaunts..."

I'll check into that - thanks.

Originality not a big deal at this point.

Thks.

Oh, by the way - here is some info that makes me question the originality of the transmission/engine combo. I'm pretty sure the transmission is not original. The reason I think so is that it has a B&M shift lever with a Hurst-like knob on it. The shift pattern is 4-speed with reverse to the left and up (I think most had reverse to the right and up). Also, the reverse lights are operated by a toggle switch attached under the dash. And the center console shift plate has been cut in half right where the shifter hole is.

Engine is a 289 4v (originally was a 2v).

Just wondering if the transmission was changed out if that would make a difference in how the starter operates.