I am not a grower but I do know a little something about sound isolation construction. What you are trying to do will be difficult if not impossible. The isolation padding you put under the mounting plate helps but it doesn't prevent the noise and vibration from transferring through the fasteners to the framing and that results in the noise in the adjacent room.
I suggest two possibilities. Build a frame out of a couple of 2x4's studs and a top and bottom plate. Place a piece of 1/2" neoprene rubber on top of the top plate and on the bottom of the bottom plate. You will want to build this frame almost a tall as your floor to ceiling height is less about 3/4". Stand it up and position it next to your mounting wall but be sure not to let the frame touch it. Then place a couple of wood wedges, at the top and wedge it snug between the floor and ceiling. Mount your fan to the fan and that should improve the sound isolation considerably.
The other suggestion is much simpler and that is to switch to an adjustable floor stand oscillating fan.
Hope this helps.
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