If your starter is turning over really slow, like a re-start after the car sits a bit and everything is heat soaked, I would suspect a bad ground or grounds. I had this problem when I first bought my car (many years ago). The wires would actually get hot and smoke even with a brand new battery. What finally cured it was taking off the ground strap that goes to the engine and vigorously cleaning everything until all the metals were nice and shinny. That lasted for many years and then I think I had to do it again maybe once... Good luck !
This is definitely related to some component i.e. starter (I've also heard starter solenoid?) or wire/wiring getting hot and therefore causing the car to have trouble cranking.
I have an OEM type larger starter. Would the hi torque mini starters be any better? My guess making a heat shield would still be required. Is that thermal shield tape a good for making a shield?