I have the same machine, and although I don't have as much vibration as you clearly do, I do suffer some. I'm 99% sure that the reason for this is that although I have the machine bolted to a pretty solid bench, the bench is mounted on castors (that type where the "wheel" looks like a solid rubber ball). I can't do away with the castors due to my shop set up, it must be moveable, but I will try different castors to see if that reduces the problem. But I'm not rushing because my vibrations only occur at a couple of certain "sweet" spot speeds (should that be "sour spots"? ;-) ) so I can easily work around this by changing speed slightly.
I must say that the EX series of machines is well-known for being vibration-free, and on the sample machine I tried before buying, which was not bolted to the bench at all, there was virtually NO vibration. So I GUESS your vibration is coming from your castors, just like mine.
So I'm again guessing that there's little point in making a new stand for it, whatever dampening material you put in it, if you're going to continue to mount the stand on castors. Assuming your existing stand doesn't wobble at all, I'd first try removing the castors and see what that does to the vibration - ideally the best way to remove vibration (assuming the stand is solid enough) is to bolt the stand feet to the floor, plus add two bolts somewhere higher up, into a wall. But like me that obviously doesn't allow the stand and machine to be moveable! Hence the idea about trying no castors then different castors as a test before going any further.
Please also note that another member here (I'm not sure, but think it was Aramco) had similar problems but solved them by putting his stand on top of something called cow mats. I don't know (I'm not a farmer) but I assume that these will be very thick rubber mats used by dairy farmers for the cows to stand on in the milking parlour or something - but that's just my guess!
HTH - no point in making a new stand if that's not the cause of the vibration