An Exceptionally Technical Discussion of AESToE
It would be straightforward to formulate a similar theory -- including gravity, electroweakish gauge fields, and real fermion fields -- using only F4 instead of E8.
A modified BF formulation of Yang-Mills is equivalent to Yang-Mills, just vary the action with respect to B and plug that expression back in. The advantage of a modified BF formulation is that it naturally gives the Dirac action for fermions, via the pure BF term for that part of the algebra. It should be very interesting to calculate how these parameters run, and how the formulation connects with approaches to quantum gravity.
Thanks for pointing out the reference.