It always harder to start when it's hot. You'd think it would be just the opposite!
I usually don't have to travel but 10-15 feet before I pop the clutch, so I don't think the RPMs are high.
I usually use 2nd gear so it doesn't jerk me and the truck too hard when I let off the clutch. Always fires right up.
The 216 has 97K on it and I have no idea what, if anything, has been done to it during its lifetime. It *does* smoke a bit while running.
Sounds like you have multiple issues going on at once, which always makes troubleshooting "fun". Hotrod is your man. He'll help you sort them out.
As far as RPM during a push start in 2nd gear (3rd for that matter), you will definitely have much more RPM than what your six volt starter will provide.
Another aspect of the efficiency of push starting and its resulting higher RPM is the dynamics of rotating mass (crankshaft, flywheel).
Physics dictates that a body in motion tends to stay in motion. The increased speed of the motion of these heavy rotating parts is what makes push starting easy to do.