I also enjoy designing and building small electronic projects. It is projects like this that I really wish I had a scope. I am in the category where I know just enough about electronics to be dangerous.
I have been using brushed ESCs for many years to control LED lighting on my night helies, you can definitely see the steps in light output as you slowly raise or lower the throttle. I do not know if those steps will be fine enough adjustment to the the air/fuel ratio correct on the pulse jet. But at least I know that I can just plug in some LEDs to see how fine the steps are. Although you can only see the steeps near the bottom end of where the LEDs are just starting to light up.

OK thinking out loud here, IF I were to hook up the ESC with an appropriate load, would a digital voltmeter be able to see past the PWM and see the steps?
Maybe have to add a capacitor to smooth out the PWM frequency before I can measure the steps?