If you really, really want to play games with gravity and base it purely on really basic quantum principles, while ignoring space/time warping, General Relativity and Einstein completely, then it would be fair game to take a probabilistic viewpoint of gravity, in the vein of Hitchhiker's Guide to the Galaxy.
That is, assume anything can be anywhere, at any particular time, without there being a defined path from point A at time A' to point B at time B', depending on some probabilistic function, without recourse to any specific time interval. That is, the world only exists in the immediate, from moment to moment. There is no 'before' and 'after', no 'cause and effect', only the 'immediate'. Then, make the probability function of a particle being in a particular place dependent on the mass of existing nearby objects. That is, the probability of a particle being in a particular place, becomes higher the closer that place is to a large mass. When the particle appears at this point, it increases the local mass, and increases the probability another particle will be there, and that this particle will be even closer to the center of the mass on the next iteration. Thus, over time, the probability of a particle being nearer a large center of mass increases, so it would appear that the particle is approaching the larger mass. In reality, what is happening is that it just becomes more probable that it is in that position as time goes on.
It explains black holes, but it does not explain the expansion of the universe. But then again, I am not sure quantum probabilistic principles alone will ever explain this. What would the probabilistic function look like for this? An anti-mass probabilistic function? That it is more probable for a particle to appear away from a large mass? Seems contradictory. Yin and yang. The ultimate cosmic tension. One probability in conflict with another.
Of course, explaining exactly why the probability changes with mass is left up to the reader.