I think my reccomendation would be to figure out how many cars are needed for your operating sessions and then add a few more. Clean that number of cars first, and then create a "rip track" either on the layout, on a shelf, or even in a box or drawer. Keep cleaning the wheelsets, but once you have enough done for an operating session, you know you can have the session without having to clean in "panic mode." When you have finished all of the cars, set up a cleaning schedule where you take off a certain number of cars every month and clean them whether they need it or not. If you set up a data base on your computer with the cars identified by number you can set it up so that you cycle through the cleaning process a few cars at a time continuously so that you never again find yourself having to clean the entire fleet at once. Once clean it might even work to take 10 or 20 cars at a time and pull the wheelsets and put them in the ultrasonic cleaner for 1/2 hour or how ever long it takes and let it clean them for you. If you did that once a week, it would never again become a big chore.
Glad to hear that you are successful in what must have appeared to be an overwhelming chore to start with.