Homemade sound panels

Just my opin......I would lose the pegboard. Also, foam doesnt' transmit sound. the object is to either aborb, turning sound energy into heat, or to diffuse/reflect randomly. The 705 will absorb, since it is 'transparent' to sound. If you can't breath thru it, the foam will tend to reflect.
Mounting away from the wall is a good idea, it'll give you incoming and outgoing 'treatment'.
Again, just my opin, but I'd either make diffusors or absorbers. The local fabric outlet has a real open 'fabric' which would be good for covering 703/5 doing as you suggest, keeping the fibers in. Cover the whole thing in accoustic cloth and your there.

As a sidenote, an anachoic space is NOT what you want. I've been in a very dead recording studio and it is ...funny sounding..... Many normal audio 'q's are simply gone missing. Don't do that to your listening space.

Silicone around the edges of the pegboard or it might vibrate or, better yet, avoid it. The pegboard is the same as the wall that you're trying to get away from. If the pegboard were in front and not touching anything, that would be a membrane but not a good one.

The foam might be better aesthetically but it's less functional than double thick 705. For a single layer of 705, I would expect reduced effectiveness below 200 Hz. Double thick is fairly effective, with the air space behind, down to 100Hz.

Owens Corning 703..4-2'/2" thick...you can buy a 6 pack off ebay for under $100.00..works well if your handy with material covering

For bass traps, would I be better off with one, 4 inch thick panel (24" x 48") in each corner or two, 2 inch thick panels stacked vertically (24" x 96") in each corner? Or is there a difference?

Here are two links to DIY help:
www.ethanwiner.com/acoustics.html
http://www.bobgolds.com/
http://forum.studiotips.com/viewforum.php?f=8&sid=17689dd547daffa3ecfd9db0fe725313