We basically don't know what your using. In the diagram which uses a FET, the 10K prevents the FET from turning on accidentally with leakage currents and gate capacitance. The 100R limits the current to the gate. The FET is likely a logic FET. I didn't look it up.
Your injector might be known as a high impedance injector. From what I read, I think, the low Z, require the current to be cut once activated.
I did this to a few solenoids I used at work for shutters although for different reasons. One was a rotary solenoid that wasn't activated for long periods, so that was a traditional kick + drop to a lower voltage. Without the drop, the solenoid would burn up. Without the kick, it would not open. The other one was because there was a 1 mm expensive piece of glass nearby and I wanted slow opening, so I used a PWM chip with soft-start.