Switching to LED lighbulbs made it look better, but the flicker actually got worse, especially if I move my camera around.
Yeah you don't wanna do that. The clock speed on your CMOS is not slaved to anything unless you're shooting on something with a timecode input and the clock speed on your LEDs is not slaved to anything unless they say Kino Flo on the side. It might work sometimes? But the times it doesn't work it's going to not work really hard.