I think you would do a lot of carpentry with little effect.
I would try isolation. Alternatives include:
1. Put some foam rubber under the washer. Get some 1" to 2" foam rubber and a piece of plywood (at least 1/2") a bit bigger than the footprint of the washer. Put 12" squares of foam rubber under each corner of the plywood and set the washer on the plywood. While at it, I might do the washer and dryer together to keep the heights matched.
2. Get some fairly dense foam rubber and isolate the whole platform. Set it on isolation so there are no wood-to-wood contacts or hard fasteners to structure.