""Pressure" is a concept that is the statistical result of stuff bumping into each other and exchanging momentum via electrostatic force."
Now I know you're just trolling. You have it exactly backward.
Pressure, the concept, is defined as force per unit area. There is nothing in that about electrostatic force or momentum transfer. If I take two diamond anvils and apply force, there is a pressure at the interface but no momentum transfer. The pressure is RESISTED by the electric field of the electrons; the electric field is not the pressure.
But, going a step further, what really causes, say, atmospheric pressure? It is caused by the gravitational force acting on the molecules of the air and pulling them inwards towards the centre of the earth. The reason that the air doesn't collapse to a neutron soup is indeed that electric field surrounding the atoms, but the pressure is caused by gravitation. In a neutron star, the gravity is high enough to overcome the electron fields of atoms, and the nuclei condense to a liquid. The matter of the star doesn't collapse to a point because of complex interactions between its baryons, but it has a pressure at every point and the pressure is caused by gravitation, not by the electroweak or strong forces.
So now we have vacuum energy. Like gravitation it behaves as a field which is not mediated by photons or other particles that feel the EM force. Also like gravitation, its effect is to create a pressure on masses of particles. But, unlike gravitation which is attractive between particles, it causes a repulsion, or by extension a negative pressure. And just as the net force vector on a particle due to gravitation is in the normal three spatial directions, the repulsive force will produce a vector on a particle in the normal three spatial directions.
I'd say it is hardly rocket science, but of course our rocket science is generally on too small a scale for vacuum energy to affect orbital calculations.