The cranking speed is the same all the time.
The starter is strong and about 6 months old.
My battery is also about the same age. I've cleaned the battery conection posts and ground to body.
It doesn't matter that those parts are relatively new - test and prove they are good.
There are more - equally important - electrical connections in the battery -> starter circuit. Disconnect the battery and clean the positive cable's connection at the starter motor. There is also a medium gauge red wire there and a smaller guage black wire at the solenoid - clean those connections, too. Next there are 2-3 red wires in a junction box on the left inner fender. Clean those. While you're at it clean the green wires in the juntion box, too - those are for the alternator warning light. And clean the connections at the alternator. Finally there is (or should be...) a ground strap between the bellhousing and a metal tab in the transmission tunnel (you have to get under the car to get to it). Clean both ends of the that. BTW, I like to smear a bit of di-electric grease (aka tune-up grease) on all the cleaned connections. It helps stave off corrosion.
A compression test or leak down test will reveal any internal problems. For example if the valves are not sealing properly that can cause problems getting the engine to start during cranking yet it can seemingly run OK once started.
A no-cost idea would be to disconnect the CSI (Cold Start Injector) prior to cranking the hot engine. The CSI should not squirt other than for a few seconds during a cold start. But if it were squirting when it shouldn't, the extra rich mixture might make hot starting a problem. Just a guess...
Checking the system voltage during cranking is another quick/easy test. Connect a voltmeter to the battery and see what it reads during cranking. L-jet requires approx 10.5V or greater to wake up and send the make spark/squirt fuel signals. If for some as yet undiagnosed reason the system voltage is marginal during hot starts but not cold starts that could explain the problem. (which would then need more diagnostic efforts to figure out why but we'll deal with that if needed later)