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There is still action at a distance between bosons and mediated particles.

No. There is not. You are mistaken.

What pulls them? Every time I ask, I get the answer we don't know.

Nothing pulls them. They are the pull. I don't know who you're asking, but you are not asking physicists if you're getting this answer.

The graviton is still speculation. They haven't confirmed it yet. When it comes to gravity, it's one hell of a long pull between fermions.

First, it's more than speculation. It is a well-informed draft concept based on the behavior of the other interactions which we do understand and the large-scale effects of gravity which are quite well known. Second, agreed, it has not been detected, but that is not the same thing as speculation. The current theory -- that gravity imposes curvature on space-time -- is adequate for all but the very shortest range interactions; it has tremendous explanatory and predictive power. It is only unsatisfactory because it is not a quantum theory of gravity, but, it may even be fully correct. It may turn out that gravity is not a field in the quantum mechanical sense (I, and a great many other people will be very surprised if so.)

Third: gravity is not limited to fermions, and fourth, gravity has no more "longness" associated with its pull than the electromagnetic field, which is also infinite in its effects; and photons account for infinitely long-distance attraction and repulsion quite well. In fine and in sum, your objections are ill-informed and incorrect.

If they do find a Higgs boson, they still won't be able to explain what the fabric is that provides the resistance to acceleration.

There is no such thing as acceleration at the quantum mechanical level (mathematically acceleration does not correspond to a bounded Hermitean operator on the Hilbert space of state vectors. Colloquially, The Uncertainty Principle rules out measuring the quantities required to make acceleration sensible for a particle), so no one expects the Higgs to explain a concept which has no quantum mechanical meaning.

If you are interested in the gross properties of matter, like acceleration -- which is not quantum mechanical -- those properties are described quite well by the Equivalence Principle and the relation of gravitational mass to inertial mass; they are the same, and Einstein explained why. Having explained why, we know that acceleration is a measure of the curvature of space-time.

The Principle of Stationary Action is at the bottom of all of these things, whether quantum mechanical or classical, and whether you believe in gravitons or curved space-time (or both.) Saying that we don't "understand them" because we don't understand why there is is a Principle of Least Action is a metaphysical question, not a physical one.

Why are there laws? That's not for physicists to answer and we don't try. The Pope -- among many -- has a theory. Check with him.

Saying that physics does not "explain" Stationary Action because you don't see how a variational law can operate over the entire universe is either a problem with science, or a problem with you.

The problem with you, I am trying to help you with. Here is one analogy which may make a connection for you: Feynman Diagrams for Vector Bosons. But in any event, you are not being well served by people who say we don't understand.

The scientific problem is an ontological one, and a problem with all science: science does not "explain" anything in the deepest sense. It merely offers better and better, and deeper and deeper, descriptions. But this, again, is not because we do not "understand the physics."

We do.