Q: Having problems with car starter

My car won't start. I checked the keys, battery fuel, there's no turnover on key to ignition, checked relays on starter and changed them with my neighbors, re-flashing ECU, checked connector on clutch NSS and manually pressed it. No DTC's, no warning lights. It seems like there is no power to the starter. The car has good fuel, 13.2V on battery, and no other odd behavior. There is nothing touching ignition circuits, and it has a factory exhaust (through the midpipe. It's a boss midpipe, but it is all factory Ford parts).

I am thinking that there might be a loose connection on the starter. Here is a rundown of what happened:

key on power was good, accessories would run, you could hear the starter relay trigger when the key is pushed to start, no noise or movement from the starter, I did not look for theft light, play with clock spring, or otherwise (did try both keys); eventually on one start attempt at the very end the starter began to move. On the next start attempt, and every one since, the car starts normally.

I am thinking there is a loose wire, or something is overheating. This seems to happen when the car had been driven in the past 3 hours. Here is some additional troubleshooting I tried:

jump started the car (no joy/no change), pulled the battery for an extended period, flashed ECU to stock, flashed ECU to other tunes, adjusted the column, locked and unlocked the steering wheel, and turned it to various positions, reset the key programming, locked, unlocked and engaged the alarm of car, and then disengaged the alarm through the remote, verified good operation of NSS, checked for DTC's and found none, moved the car back and forth, bounced in it, moved and checked all fuses and relays, and then I called a tow, pushed the car out onto the street for loading, and then it started.

It has started every time since the last occurrence. The dealer feels they may have to charge me a diagnostic fee, and that they may be unable troubleshoot it if it doesn't happen while it's there. Are there any other steps I could take to fix this?