Alright, I may be a complete newb for saying this and I know it's feeding the addiction, but looking for your honest expert here.
But is there some reason that fibre count is so important?
I'm not selling that bread, but there is a lot of talk about low-carb dieters not getting enough fibre. For the most part, products that net carb have bran or corn fibres. Fibre can also come from fruit flesh and pulp (which is usually out) and vegetables (which I'm reading here is more and more taboo).

The sincere question becomes: Where does the fibre come from in your diet?