How about pressed carpet remnants in the same kind of compression butt? Anybody tried that?
Yes! It works quite well. We use compressed carpet at our archery club. But our broadhead targets are about 6" narrower than the others to allow the broadhead to pass thru to the other side. The only down side is you either have to un-screw the broadhead to pull the arrow out or pull the arrow straight thru which is hell on the feathers.
Fiberboard without tar is available.
It certainly is! That just happens to be the industry I work in. Just about every bowhunter at work has his own fibre bale in his back yard or basement. They are very durable , easily constructed , and if compressed to the max , most fast bows only penetrate 3"-6" which makes arrow removal easy. The trick is getting the right fibre board. I've found that fibre board containing virgin kraft is too hard and rough on arrows. Fibre board with solid chip made with water based adhesive is what you need to look for.