That's a heck of a speed for such a heavy drum!.. I don't think adding any fluid to it would help much with that kind of weight.
What are the approximate dimensions of this drum? My mental image of it is about twice as long as it's diameter (otherwise you'd call it a pipe), probably a few feet around, a couple inches thick to get to that weight, with a pretty big shaft going through it... Correct any of my assumptions please!
Perhaps if you could mount each end bearing on a load cell you could monitor the vibration as you rotate it, and add/subtract weight as necessary to get the right balance?
I'd use an Arduino, and have 1 sensor that fires once per revolution, and each load cell connected to it... from there, you can have the Arduino calculate how many degrees after that sensor fires it hits the peak load, and figure out where that relates to on the drum.