This is not a question for an Einsteinian, for sure. Neither is this answer.
I picture this as a universe that is encased in an infinitely large torus, such that something would fall forever, while circling around. However, this image is not absolutely necessary for the solution.
In quantum field theory, it is implied that the fields occupy the universe, equally, and are equally distributed throughout. The fields never move in this universe. That is, they are static. Okay, hard to quantify when field theory is point-oriented, but nonetheless.
So the air molecules in your universe are just very large special bosons, which are captured within the 'net' of a corresponding field. This field, like every other field, fills your infinite universe and is static. In terms of the torus, it 'fills' the torus and defines its shape. 800
Think in terms of this 'field' making the torus 'solid' or 'frozen', as an allegory. Everything moves in this 'solid' (field). The air molecule bosons can not move within this 'solid' stationary field, as there is no mechanism for their movement. They are a field unto themselves, independent of the other fields that are responsible for movement (gravity, mass, the Higgs boson, electromagnetism, the strong and weak fields, etc.) However, the independence is not absolute. These molecules also contain Higgs bosons on steroids, which therefore add 'mass' effects (inertia), and thus air resistance for terminal velocity.
However, the theory behind this would require a physics textbook much, much thicker than the one we have today. One in which <PERSON> was but a footnote. It posits a boson and a field which, frankly, we haven't even conjectured.
The fact that these bosons are uniformly distributed, explains why there is no increasing pressure. These bosons, as I stated, do not interact with gravity nor do the molecules contain any bosons that DO interact with gravity.
Edit
In this scenario, I envision your 'islands' to be like asteroids, which would have their own slight gravity, but the movement of everything around the torus would not be due to gravity, but some rotational force, like a particle in a toroidal magnetic field. Again, another boson and another field, apart from gravity. 800