Antoine, your CXL PN has a geared belt? Those PN's are exceeding rare and hard to come by! Not many of those were made for too long before Aerus Holdings bought TriStar and came out with the EXL. You might want to look into acquiring a spare brushroll, motor and geared belt to have as spares, as those parts are hard to find now....they may even be discontinued. In that case, used parts is all you could do, and the motor possibly there's a new one that has the same gear spacing that could match it? In fact, I do believe one of the Beam powerheads that Electrolux AB produced might have a motor with similar enough spacing between the teeth on the motor spindle for the belt that it might be able to be used in a TriStar CXL geared belt PN.
While you're at it, I would also suggest contacting Patriot in California and buying a couple of the wand adapters they put on the generic PNs like the Douglas PN to adapt them to use with TriStar style wands. Not only so you can use other powerheads in the future, but it also helps with being able to use generic buttonlock wands. And btw, your local vac shop that deals with Hibbert International, JohnnyVac or Tip Top Parts Canada should be able to sell you a carbon brush seating stone, they are stocked by those distributors.