" ... an electron's rest energy may be too small to measure as a gravitational effect on a macroscale, but two electrons hypothetically in a background independent void whose gravitational field boundaries overlap in the least, would mutually experience the asymmetric directional tendency as would be called 'attraction' in the classical Newtonian paradigm."
No, John R. Electrons (and all fermions) are not mutually attractive; they repel each other in all cases except Cooper pairs, in which electrons cooperate in their spin states and become superconductive. That's not gravitation, though -- it's definitely a quantum electrodynamic effect of energy exchange, even though the behavior mimics bosons under the conditions in which Cooper pairs form.
A plausible exotic theory of gravitation is the case of boson stars that Steve brought up. I have no opinion on it, though what makes boson stars plausible is that any number of bosons can occupy the same space, i.e., share the same state of self interaction. No two fermions can do so.
I didn't catch the NSA reference the first time around. I must be missing some history here.