There is a technical bulletin out on 2000 to 2003 3.0L that says some may get a " buck/jerk and miss during drive cycle" Mine gets this random jerk/ buck every now and then. the bulletin says it will not produce a code or CEL and this is the same on mine, no CEL or code. Also I get a bit of chirp type noise when cold just after start up but goes away, again random,not all the time, and it is not the belt.
This pretty much leads me to believe it is the synchronizer. not the cam sensor attached to the top of it. I believe what happens is when the gear gets some wear in it, it then can buck a little do the the extra slop and this gives a wrong reading so the injector fires at the wrong time and in turn produces the buck or jerk.
I believe you had the sensor replaced, but it is the synchronizer that the bulletin refers to as the part that goes bad.