[scaleslotcars]

This is a common fault on clamshell Scalextric cars.
It is caused by the underpan distorting with age and the pinion then jamming on the contrate as you described, you can try twisting the underpan back into shape with the aid of a little heat, but this is rarely successful.
Better is to remove the pinion and then remove the small spacer that is behind it and then replace the pinion so it is then further along the shaft, this should give you the necessary clearance and the car should run fine.

 

[scaleslotcars]

Your partly correct! the 222 has the same shaft diameter as a 111 and uses the same contrate, the RX has a slightly larger diameter shaft and uses a different contrate.
This was one of my first thoughts on the problem, as he had used parts from his spares box, but he says "the 'lips' on the contrate that centre the motor shaft are jammed solid against the motor pinion" which sounds more like the pinion is too far up the shaft, but then again it could be a combination of both problems, difficult to tell without actually seeing the car.

 

[scaleslotcars]

There is another method which I have successfully used in the past, a little easier if you have limited tools or abilities.
You can pack a small piece of plastic between the motor and the chassis which will force the axle carrier back a little freeing the contrate from rubbing on the pinion, picture below will show what I mean.

QUOTE "Is the lighted version actually marked E/2?"
No none of the 'E' cars were marked as such on the underpan.