I identify four possible kinds of thrust below (there may be more or less). I don't know how to do the math to test them though.
Direct transfer of kinetic energy as thrust. The energy of objects falling into the black holes themselves would transfer some kind of directional force, right?
Ion thrust. Radiation/gases emitted by the black holes would act as a kind of thrust, right? I know that current models indicate an outflowing of energy from a black hole, a sort of constant flow. Is this outflow constant over the whole surface of the black hole, or is it more concentrated in some areas vs. others? If so, it might act as a form of constant propulsion, causing the black hole to accelerate over time.
Gyroscopic thrust. I'm a little less clear here, but my understanding is that most black holes are constantly spinning. Could those be acting like gyroscopes and the gravitational energy of the matter spinning around those black holes acts as torque, causing the gyroscope to accelerate in a single direction over time?
Heat differential. Are black holes a constant temperature across their entire surface? Or is there a heat differential in various areas, and could that heat differential (if real) act as thrust?
Taking the logic train further: (Feel free to poke holes, I know I make a lot of assumptions, probably based on fallacies.)
If any of these forces exist, the propulsion they exert on the black holes would be immense when factored over time (even taking into account the extreme mass of the black holes themselves). In fact, if these forces exist, it would stand to reason that the more massive a black hole is, the faster it would be accelerating in space.
Then, if black holes are accelerating, in what direction? I'm guessing they would generally accelerate away from the largest concentrations of mass, the impact of the mass itself propelling them in the opposite direction. I am less clear on the directional thrust of the radiation emitted or of any gyroscopic thrust.
But, if the supermassive black holes accelerate away from the largest concentrations of mass, then, over time, they are moving away from the center of the universe at an ever-increasing speed, right? This is assuming that mass in the universe is most dense at the core and least dense at the edges.
And, as these black holes move through space, they drag their respective galaxies along with them. Acting as galactic engines, propelling the expansion of the universe over time.
Lots of logical leaps, I know. But it was a fun ride.