One sure way to have fiber-packed “real” bread (actually, fermented) is to make your own. I write about this in my book, FoodWISE, and share how I used to make (and freeze) 20 small loaves a week.
I’m back to making bread, and this time with home-milled wheat berries grains (white and red wheats). I use the “Mockmill” attachment to my Kitchen Aid, as does Steve Jones of WSU’s Bread Lab.