Bad cam shaft senser

Check the fuel pump emergency cut off just in case also may want to look at the ECM..

disconnect the shifter from transmission when cold and try manually move the shifter at transmission when hot if sticks or binds something happens at the shifter shaft

Buy the sensor from the car dealership. The sensors at auto stores are inferior and sometimes do not work properly.

You did'nt say if you have had the car (Scanned) to see if the engine control Module has stored any fault codes. You say it runs 20 miles or so before it quits. After cooling does it alawys start back up? What have you been doing to get it running again? The ECM can warm up and quit. It'll get an Troblem code about though. The no spark at the time sort of removes the Cat converter overheating and the ingtion Module ( (the coils are mounted to it). Something getting too hot is likly. Crank sensers and cam sensers both wil do this the crank senser is on the back of the block just above the oil pan. The cam sewnser is underneath the power steering pump and the connector going to it is on top of the front valve cover on the passenger side. Crank sensers will not code and still be bad. Computers if they come back on ever they will code most any problem and the code name is Quad driver failure.

Possible partially plugged catalytic converter? The pop may be unburned fuel igniting. I would want to check the exhaust manifold pressure. Have a helper hit the gas pedal and back off several times and feel the exhaust flow, if it doesn't seem to increase in relation to the engine speed increases, and/or it gets extremely hot, compared to a normally running car.that is a good indicator of a plugged cat.
If you also get a pop, especially if it includes a burst of exhaust as, that is an additional indicator.

replace the cam shaft position sensor

the TPS senser is bad its on the injecter pump or you have a bad crank shaft sonser

The ignition coils are the usual culprit, they fail when hot, sometimes the module itself is bad, you need an Ignition specialist here, don't Shotgun (Replace parts till it runs)

The check engine light should be on with the engine running. The coolant temperture senser may be open at some temps the fastest way to test this is to change the senser ( it's cheap and a high failure rate part all auto parts stores will haveplenty of this high failure part in stock and they fail many ways. If the car ever overheated it's damaged or truly bad. A very good one will optimize fuel mileage so if it's suspect change it anyway as money well spent a working but wrong senser can cost alot of gas on any fuel injection car or truck, You get what you pay for in temp sensers and the brand name ones are better. All of them are suspect to be bad even when new and ohm test at temperture charts are is repair manuels. Crank sensers and cam sensers also get hot and quit they cost more are harder to change and fail more on the 3.8 motor than the 3.1 or the 3.4. Igiton modules do this too but it sounds like its been doing this awhile and modules and crank sensers don't stay half bad very long. they stop altogrther. Temp sensers can stay bad and work wrong. If you can get a scanner hooks to the car on data stream the senser may show room temp when cold but as it heats up goes up then to -34 thats open the system doesn't know that to do as the air charge temp senser doesn't agree and the system fails to start and will check as flooded. Flooring the gas and hoding it there may start it anyway. The trottle position senser were to show open thats the clear flood mode and the injectors won't fire. Tps voltage should show .5 volt les than 1 volt at idel (it'll start) and 5 volts at full throttle or nearly. if it shows with a scanner of a voltmeter on the center wire 5 volts or 0 it won't start. Coolant senser fails more often and is cheaper

What happens when it sits for a while, does it start back up & go ?