Ok, I'll just tell you what I would do and it's not the "exact perfect way" but I think it would really work.
I'd go buy several rubber shims or PVC shims. I'd stick SEVERAL under it in multiple places. Get a solid foundation of support.
Then I would buy the expanding foam "great stuff" and spray it in all the nooks and crannies (avoiding drains and cracks). The foam expands well and is fairly solid. It may back up the shims for support especially with the expansion. Think of it like a solid platform of hard foam with many heavy supports through it (shims).
Anyway, that's what I would do. Unless you can find a very solid thick piece of rubber and cram it there underneath.
Anyway, THINK SUPPORT.