How about a base made entirely from conveyer belting.If one could obtain it cheap enough, a plant closure or a revamp of equipment at a plant.
Obtain about 50 feet of conveyer belting 36 inches wide or so and for example 3/8 inch thick. Next, cut it into 4 foot long lengths.
I know this would be time consuming! Obtain a good degreaser to clean the belting and get down to clean rubber. Buy 1 gallon of contact cement. Glue the 4 foot strips together so that you have 11 pieces making up a thickness of a little over 4 inches. This would then be sandwiched in between channel iron.
For mounting the engine and generator, 4 pieces of 4"channel,4 feet long with the hollow pointing down,top and bottom. 6"x 3/4" bolts every 12" or so. Distance apart would be determined by Listeroid mounting hole dimensions.
4 pieces of 6" channel ,5 feet long would be used on the outside for mounting onto the floor. Hollow pointing up at the top and hollow pointing down at the bottom.
Getting back to the 4" channel,it might be better to have the top pieces pointing up,and then weld pieces in for mounting the engine and whatever your driving.
This would be one huge vibration dampener. I can imagine 1 foot of 36 inch, 3/8 thick belting would probably 5lbs or more!