Very, very nice quilt. And thanks for the info on birthing a quilt. I've heard of doing that to a quilt, but had never heard calling it birthing before. I would just bind it as is.
I don't know what birthing is. I would quilt it with a thin, stiff stuffing like that cotton-bamboo mix, or maybe just back it with felt. Fold down and stitch the edges with a little felt showing.