- R2 is likely to cause more problems than it would solve. I would get rid of it, but see the next point...
- The emitter of the BJT won't go above about 2.7 V. If it did, the base-emitter junction would be reverse biased and the transistor would be off.
- Look into opto-isolators/solid-state relays. You should have no trouble finding one that is through-hole and can work with 3.3 V and a single resistor. EXAMPLE There are also gate driver ICs for MOSFETs that can work off 3.3 V logic. These often provide their won charge-pump so you don't even need to provide the 5 V (or whatever) yourself.
If you can't invert the PWM logic, you just need to add an extra transistor. Something like this could work:
simulate this circuit – Schematic created using CircuitLab