Yeasted multigrain is a wee dram spongy-gritty

I've been baking the yeasted multigrain recipe from Crust & Crumb, in sandwich loaf form, for a few months now and while it keeps getting better, I'm still yielding a slight gritty-spongy crumb. For grains I use rolled oats, polenta, flax seeds, wheat bran, and bulgur. The only thing that differs from the recipe is the barm starter I use, rather than the suggested biga, though I did attempt it once with the biga and found the barm to be nicer.

That said, my question is: What can I do differently (or avoid) to make the crumb slightly softer and not so gritty-spongy? Before baking, the dough is moist and loose, rather than dry and tight.

Thanks,

TS