[LMP]

"the RPMs drop and the engine seems to vibrate. I can let off the gas - it stops and I can accelerate again "
THis is most probably TOrque Converter Clutch gone haywire, a classic. THis is expensive replacement cause transmission has to be taken out. However, simple thing to do is disconnect TCC solenoid by taking one contact out of connector...you will not have TCC anymore...spoil about 2mpg ON THE HIGHWAY (no change in city driving) ..but no vibration.
I think you have changed A LOT of parts ..not sure why...was all of that ruined on a sudden?
No start indeed points to Crank Position Sensor. TO be sure, just have someone check for spark when it fails starting. However crank sensor has 2 parts..and you can have spark and no fuel injectors....
About hydrocarbons: the change is probably due to the great numbers of components you have replaced..changing operaiont conditions ..possibly higher fuel pressure than before ..and computer must adapt...(lessen injection duration) if it can: for this it needs a well functioning O2 sensor: this is probably what has failed....but other culprits can be: failed catalytic converter...or/and EGR valve....
DO y9u have the Check ENgine Light ON? Did you have code scan performed lately? (seems they do it for free at Autozone)