Damping is the key word and adding mass is the key to calming the damping effect. It would add significant weight but building a concrete form to pour about 2" to 3" thick block just larger than the generator base. You will need to carefully position 4 holes in the block just to keep the genny from dancing around. You still may be able to use the feet you are showing.
In my prior life I had 3 large squirrelcage, combustion air, blowers about 50" diameter, driven by 75 hp motors. The shaft bearings were mounted on fabricated steel frames about 4-1/2ft. tall, made of 5/8" welded steel. I could not keep the pedestal bearings from self destruction, no matter how carefully the fans were balanced. I finally had holes burned in the side of the pedestal housings and filled them with concrete. Had lots of non-believers but this magically solved the problem.