Ford Escape / Hybrid :: 2004 2WD Stalls Out - No Codes

2004 Ford Escape 2WD 3.0L with about 81,000 miles.

Problem: 2 possibly related

1) If warm up (get to about 190+ degrees) and then cut off engine. Does not start. If I wait about 30 secs and play the gas pedal, then I can get it to start with high revs and after about 15 secs runs normally. Or, I can disconnect the air intake and it'll start fine. But if you stop and try to start again, no joy unless playing with gas pedal.
2) After driving about 20-25 mins, it seems to randomly stall-out while going about 40 mph. When it stalls out, it will restart again after about 30 secs.

Note: Neither of the above throw any codes.

Here's my problem chart after mining the other posts:

Thing to replace/do //// No Code /// Stall while driving /// Won't restart when hot
Fuel Pump //// Yes /// Yes /// Doubt it
Fuel Filter //// Yes /// Yes /// Don't think so
CKP Sensor //// Yes /// Yes /// Yes
CMP Sensor //// Unlikely /// ? /// Possibly
ECT //// Maybe? /// Yes (if too hot) /// Yes
IAC Valve //// Unlikely /// Yes /// No
Thermostat //// Yes /// Yes (if too hot) /// Yes
MAF sensor //// Unlikely /// No /// Yes

What I've done:

- Well, I started looking at the vacuum lines and they were crumbling so I replaced all those (to EGR and all that).
- There is a mystery line that appears to come up from the canister and go to nothing--is this some kind of atmospheric vent?
- My cheap scan tool also shows engine temps getting up to 216 degrees if I make it work (idle high at 2000+ rpm), so I'm suspicious of the cooling system and thinking maybe the ECU is shutting down to avoid overheating.

I'm going to start with flushing the coolant and replacing the ECT and thermostat while doing so. This is relatively inexpensive and ECT can do weird things. The restart problem is consistent, so I'll know if I fixed that right away.