PATS works by disabling the fuel injector pulse. For the 1996+ model year the Ford factory PATS does NOT disable the fuel pump.
So by that measure it would not be possible to defeat PATS by simply using starting fluid as the PCM would never fire the injectors. The best the starting fluid could do is run the motor until the starting fluid has been exhausted.
Regardless. You could answer your own question by noting IF the theft light goes out after the 3 second "prove out" that happens at initial key on. Do this on the restart attempts. Don't be in a hurry to crank it.
The other thing about Ford factory PATS is PATS will never disable the motor once the motor has started.
I'm a big believer in Occam's razor. I agree that once the problem is located there will be that "light bulb" moment where everything will fall into place.
https://en.wikipedia.org/wiki/Occam's_razor
By your own admission there was an apparent ground problem that might have been addressed. However I didn't get a strong sense of what was found and what was repaired. I also didn't get the sense that once the grounding problem was repaired that trouble shooting was restarted from the top of the decision tree looking at everything anew (since a repair was made).
IMO the other outstanding question is "what is the fuel pressure"? Perhaps more importantly. Is the PCM getting an accurate fuel pressure as the FRPS could be ok but there be a problem in the wiring (didn't you have a DTC for a FRPS circuit malfunction?)
At the risk of hurting feelings, if you had an ODB2 scanner this might have made very short work of this problem. For the cost of parts already installed (without a fix) a budget priced scanner could have been acquired. Fixing modern PCM driven cars is a data driven undertaking. But trouble shooting is a "process". Sometimes it's necessary to come up with a theory and then either rule it in or out with test results or other methods.
ForScan ODB2 scanner w ELM327 USB
https://www.stangnet.com/mustang-forums/resources/forscan-odb2-scanner-w-elm327-usb.57/
Note an ODB2 reader and scanner are not the same thing. A reader will only access DTC codes. Where as a scanner can access operational real time PID's.
The added benefit of having an ODB2 scanner is that it can answer other questions such as what is the MAF value seen at the PCM? In some of your earlier posts you were asking questions about which sensor could be turning off the fuel pump after the motor is stated. The closest I can think of is the MAF. For example IF the MAF were way under reporting the air flow then the fuel injector pulse width would be too small (too little fuel).
Other sensors that "might" play a role in this is the cam sensor. We know the CKP sensor is working or it would never start. But maybe the PCM using to cam sensor to determine IF the motor is running. However I personally don't have a lot of faith in that theory because I know that a bad cam sensor will not prevent a 4.6 V8 from starting. Note a bad cam sensor will prevent a V6 from starting.
If looking for an out of the box suggestion. Since there have been grounding problems on this car, test and CONFIRM there's a solid ground at the MAF. Test the ability of the ground to carry current all the way back to battery negative. Recommend using a test light that will apply some load to the circuit.