I have a large layout using 2” extruded (blue) foam. It is as quiet or quieter than the traditional Homosote and plywood. Here was how:
I have worked with acousticians over the years. I learned that dissimilar materials can often cancel out resonant frequencies. Without that, the foam acts like a drum, magnifying the rumble.
The solution I used was to bond thin doorskin plywood or thin Masonite to the underside of the foam panels creating a composite assembly. That assembly will span more than 32”; the 1x3 framing or heavy plywood top is unneeded. And the noise is nearly silent - trust me! An added benefit is switch machines and wiring can be screwed firmly to the underside of the assembly.
It works; saves time; results in a much thinner deck. Try it!