Starter problem in hot temperatures, Starter with different number of teeth for the same car?

Hello guys, I don’t understand something.
I have a 1969 Cougar XR7 with a 351W and FMX transmission. When starting with a hot engine and high outside temperatures, the car won’t start. It feels like the battery is empty. After a while, it starts.
I’ve already had the battery checked, replaced all the ground and positive cables, installed a new starter relay, new ignition switch and a refurbished starter. Always the same problem but I’m now sure that it’s the starter. Now I thought about installing a Hi Torque starter from Powermaster and I see that starters with different numbers of teeth (9 to 11 teeth) are offered for my car with a 351W, FMX automatic transmission and 164 tooth flywheel. How can that work if the axle distance and the outside diameter remain the same? As far as I know, my original starter has 9 teeth!
Is the tooth shape specially adapted for the different starters, the axle distance to the flywheel remains the same?
I don’t know if I should order the Powermaster 9403, 9503 or 9603 or does anyone have a suggestion for another model or brand that they have had good experiences with for a long time?
Rockauto had a Remy 97101 that is supposed to fit but it also has 10 teeth instead of the 9 on the original!
Thank you for your support, here in Austria (Europe) it is difficult to get competent information.
Jonny

I also have a 1969 Cougar XR7 with a 351W and FMX transmission. I used the rebuilt Remy 25216 (RockAuto) on mine. No problems with fit or function. It has a 9 tooth pinion.

Thanks for your tip!

I too have a 69, 351W and FMX, but I have long tube headers. I had the same problem with restarting when hot. I installed a starter insulating blanket from Jegs (I think), and haven’t had an issue since.

Thank you!

Back in the 70’s we “rebuilt” the starters ourselves. The wear out parts tend to be the drive, brushes, and the front and rear bushings. I never had to change the bushings in any of mine, just the brushes and drive. Yours may just need new brushes, or maybe the brushes are sticking in the holder.

napaonline.com lists the parts to rebuild your starter. You may be able to get them to ship to Europe, or find them locally.

I had already replaced the starter with a reconditioned one from Rockauto, as I had already dismantled and reconditioned almost every part of the car. I wanted to save myself the work of repairing the starter and finally go for a drive. I have now solved the problem with a HI-Torque starter, which I had to rework in diameter, but now the car starts even when it is hot.
Thanks for your info!