So the switch-mode constant current drivers shouldn't be pwm'ed?
The answer is more complicated. Some smps are specifically designed to be pwm'd - they typically come with an on/off pin. Others are not.
So are you saying the ZTX851 would be better to use than a logic level mosfet but still not better than getting a constant current source with a dedicated pwm pin?
ZTX851 isn't a good part. The drive requirement for 300ma Ic is quite substantial for a mcu, and if you cannot deliver that much current, you see Vce going up and power dissipation up.
I would go with a to220 mosfet, just to be safe.
Can I build this circuit instead of buying a different pwm constand current driver?
You can, with the understanding that if you are using a mosfet as the regulator, leave it 1v drop at least.