I'm a fan of straw bale platforms--nice and thick insulation. It won't mold IF kept dry (ie, don't let water pool on it, make sure water drains away from your platform; potenially seal with stucco). I don't think you could easily use this for your framed platform though.
Sheep wool might be an option. Somewhat spendy but there are a couple places that market it as such. Often treated (w/ simple boron salts) to deter wool moths. Naturally flame-retardant. Available loose or in batt form. Some small local sheep farms might have a bit stashed away available (may not be washed or processed or treated)--contact your local sheep shearer for names.
I've also seen websites selling hemp insulation, cork insulation, shredded newspaper/cellulose insulation, cotton/denim insulation. I know cellulose is often used, denim sometimes used in normal construction.
There's one or two manufacturers that claim their glass wool or mineral wool is eco, for what that's worth. I count eco as something that *will* mold/attract critters, in the right circumstances. The trick is to prevent those circumstances (moisture accumulation, mouse access/population).
barriers, keeping things off the ground away from water/mice, getting a good mouser cat, wormwood to deter moths, are all ways to prevent said circumstances
You might also consider a different platform style--a slab foundation under a raised platform would allow you to entirely enclose the slab (effectively preventing critter infiltration), place whatever type & quantity of insulation you want down there, plus give you storage space.