Hallo John,

1. I would use a 12V motor, not a 24V. Running a 24V motor with only 12V is not a good idea. Or is it designed for 12V use?

2. Do you use free wheeling diodes?

3. Do you use a snubber circuit?

4. Do you use power supply decoupling directly at motor?

5. How did you found, that '5kHz is to small for the motor'?

6. Using MOSFET does NOT necessarily mean, that you have something very fast! Power MOSFETs can have rather large gate source capacitance of some nano Farads, which must be charged and discharged by the driver (driver of MOSFET). If this is done by a simple transistor circuit, which is NOT fast, MOSFET will no longer be fast, either. MOSFET must be driven by a very fast switching transistor, which drives MOSFET very low ohmic, in order to charge and discharge gate source capacitance of MOSFET very quickly.
Assume 5nF gate source capacitance and 10kOhm source resistance, then MOSFET shows a delay of 10k x 5nF = 50µsec. This is a terrible value, if you plan to have motor driven by 13.3kHz PWM. Remember that period time of 13.3kHz is 75µsec!!!
What you need is a switching delay of much less than 1µsec. In combination with assumed 5nF gate source capacitance source resistance should be less than 200Ohm.
I assume, that your MOSFET is not driven so low ohmic, this I conclude from your information, that only 0.04mA is drawn from CMOS inverter.

So, my advice is, to use a fast industrial motor driver integrated circuit, and not a self made circuit using discretes, if you want to make PWM at 13.3kHz.

Kai