What is the driest, brownest bread that I can make for a stuffing?
Any bread can be dry - slice or cube and put it in the oven at 140F, or low, until it's as dry as you like.

Wonderbread is not even bread, in my opinion - it's certainly not anything like a yeast bread, even one made from all white flour. So it's not hard to be very different from it. As such you might want to heed the advice in comments to scale back your reaction a tad.

For a different approach to "very brown bread" look at Anadama recipies - much of the brown there can be from the molasses, but you can also whole-grain it up as much as you like - but 100% whole grain and some tendency to crumble go together in my experience, so I'd probably limit the whole grains to 25-50% of the flour bill, tops. I quite happily mix and match the whole grains as well as bean flours, potato flour, etc.