Same problem w/ my 2002 3.8L T&C. Engine would miss occasionally, then run fine for weeks, after several months started missing regularly, and seemed worse at certain rpm's, finally became almost undriveable. Only at the end did it start to leave code, 1391 = crank sensor. Only a rare "ignition misfire" code previously.
I replaced the crank sensor w/ no improvement. I only did so because it was accessible (barely) when I removed the coil pack to get at the coolant temp sensor (another issue). I figured this might work if the plastic tab on the sensor was bent. I could barely see it under the exhaust cross-over and a "2-finger" job. Cost ~$14. Probably better to remove the battery tray for the same effort and better access by reaching under the exhaust pipe from the side. It mounts with one bolt, 10 mm wrench. I used a racheting box wrench, a smart investment for work on tight FWD cars (Craftsman ~$35/set). Getting the connector off is harder. You must push the red lock tab sideways first. I would re-install it "un-locked".
I was pretty sure my flexplate was cracked, due to sheet-metal noises, and others have said that is what messed up their pickup. I just pulled the transmission (very hard, especially since AWD) and the flexplate has small cracks around the bolts, but hasn't separated into 2 disks as others reported, apparently nothing to affect the crank pickup slots ("toner ring") welded to the OD.
What I did find when I removed the exhaust cross-over was that the wiring harness pressed against the backside was burned thru. I could see the copper of one wire (org?). While this harness appears to be beyond the crank sensor, it still might affect its signal by drawing down supply power or such. Other people have reported this was their problem. The crank sensor is 3-wire, so probably requires power (ex. Hall-effect sensor), rather than 2-wire sensors like the"variable reluctance" type (Ford EDIS). Note: only V-6 engines have the cross-over pipe (2.4L dropped ~2001, all V-6 since).
I will get a wiring diagram and verify "root cause" before re-assembling. I have been fixing cars too long to stumble in the dark. I will also rebuild the tranny since have it out and don't know its history, it seemed to start slipping on shifts, plus van has 158K miles. Interestingly, the trans was missing several mounting bolts, 2 were lose, 2 snapped off, and 1 jammed cross-threaded. Since <1% of owners would remove a tranny like me, most likely one of the "professionals" my wife always suggests I go to. I have an MS in Mech Engr but she doesn't trust me. Unfortunately, she never owned a car before we married, to experience professional work first-hand.