I have tried the ground thing also, from a 4:1 balun feeding a 160 meter full wave loop, ungrounded or grounded it had the same amount of static noise.
Wavrider, that was my experience too.
This is my theory on grounding for static. IMO static is pretty much static (still and tending not to flow) until a differential in potential comes close by, like touching a metal door knob or your cat's nose on a cold day in winter, then you might see a flow.
Its magnitude is very small and thus needs to be very close with a very low resistance path in order to flow. An antenna is not necessarily that low in resistance, and neither is the mast for sure. However, parts of the feed line may be much lower, and thus we can have a differential. If you ground the feed line shield, it may be able to minimize static back to the transmitter somewhat. The antenna ground and the mast are typically too high in resistance, and thus we see a path, but little to no remedy.
I can't be categorical about static elimination, but I think this is partly why the YouTube video guy I mentioned above was successful at stopping his static right before our eyes and ears.
There is more to the possibility of why I wasn't successful trying the same thing, but if I told you, I'd have to have you sent to Guantanamo.