I found a solution.
My original blueprint was a Pawn. I had to create a new Character Blueprint, and copy over the components / formulas, etc. This way, I was able to abandon the Projectile Component, and have a Character Movement component inherited automatically. Then, I was able to use Add Impulse on that Character Movement component.
I forget what settings I had to tweak in the Character Movement component (I feel like I set the default movement type to Flying?), but I do remember that I had to make my mesh physics-enabled.