I've baked the Tassajara breads ever since the first edition was
published (there's now a 25th-anniversary edition, where DID the time
go?). I see you're using the larger amount of oil recommended in the
original version (the anniversary edition formalized the lower
amounts of oil & sweetener from the range suggested in the original
book, and also half-sized the recipe!) You could try a little more
oil and see the effect.
To round out your complement of grains, consider rolled oats, millet
(can be used whole, nice crunch & interesting look to the bread),
amaranth, quinoa, semolina (pasta flour), garbanzo bean flour
(chickpeas). Sesame seeds, while perhaps not strictly speaking a
grain, can make a nice contribution.
The biggest change I've made in approaching this recipe, though, was
sparked by a conversation here on the list about "rehydrating"
ingredients. It made me think about adding those whole grains late
in the recipe. I have switched to adding the rolled oats into the
starter (reducing the flour by approximately that amount) as well as
anything like cracked wheat or bulgur. I have not had trouble with
gluten development, and the extra time in a damp environment has
allowed these ingredients to blend in more with the remainder of the
recipe. I suspect I'm using a bit less flour when I'm moving from
starter to kneadable dough with this approach, as some liquid now
resides in these ingredients, but I can't prove it as I'm more of a
"by-feel" baker and rarely weigh my ingredients. But try switching
things around and see if it helps you.