To avoid nasty fiberglass insulation altogether, I havee been experimenting with Cellulose insulation. It is normally blown into attics with special equipment, but is just as easily handled with a big shovel. Cellulose is cheap, non toxic, fire retardant, light weight, soft, pleasant to work with and, best of all, made from recycled newsprint.

I have up to now been using fiberglass between the floor joists, but see no reason why this wouldn't work. It might even be better.

To keep the Cellulose from falling thru the joists onto the ground I first install a layer of pegboard.
Before laying the joists I nail 6" wide strips of peg board underneath lengthwise, centered on the joist so a couple of inches sticks out on each side, to form a shelflike protusion.
Then the joist go in place, and I loosely fit 13-14" wide sections of pegboard in the cavity, resting them on the shelf. It is better not to screw these pieces in place, since hardboard is not particularly dimensionally stable. Just let them float so they don't buckle up when it is moist. Overlap the 8' pieces a few inches where they join. All the little holes should provide adequate ventilation.

Open up a bundle of Cellulose in a big container, like our 75 gal stock tank. Break up the lumps with your hands or a rake. Shovel it in. Done.

Some settling is expected so pile it up a little higher than the top edge of the joists. Apply your vapor barrier, then nail down tongue and groove plywood.

You'll want to keep the Cellulose from getting damp in case you have a plumbing failure sometime in the future, or rain before the roof gets on. The vapor barrier will help, but to lessen the chance of moisture infiltration, you could caulk the plywood seams and slop down a thick layer of latex paint. I get mine cheap at the hardware store, where they have gallons of mismatched colors sitting around.