When the vise vibration is reduced, it will give a much smoother drilling process. There is no problem in sharpening the drill bit. It's very nice. Even though it is with spiral grinding, this is all. As a craftsman lathe leveler, I find your application successful within the possibilities and difficulty of video shooting. The important issue is good. get results.
Sharpen on a bench grinder. Check that the point is central and the flutes have the same height by holding the drill up to the light. Slow down the speed and keep an even pressure. Drill all the way in one pass. Very likely this drill cuts oversized because he didn’t check the point is central.