Hi Coline,
After calculating you should use the 14T pinion if you require a 13:1 gear ratio. That is assuming that your new 501x has a 18T centre pulley and a 36T diff pulley??
I have also had people saying I am geared wrong, the main question here is what do you want from the motor and batteries? Long run time or geared to the moon and hope it lasts 5 minutes?
Manufacturer recommendations are good and should serve as a good starting point, making small adjustment should it be required.