There are two distinct paths to a rebuttal here.

1. Let's assume the unitary dynamics is completely sufficient for constructing a theory. In such a theory the outcomes that our life tells us happens does not happen in the same sense that we have. That is, our experience is a massive illusion. In contrast, dBB gives us a story that fits exactly with our experience. This strikes me as sufficient reason to side with dBB, but certainly it is a personal choice.

As analogy, consider the Library of Babel, perhaps thinned down to only consistent histories. dBB is the statement that there is one true history in the library and is a procedure to find it. The unitary theory is saying that they are all true and you can find the one that speaks to your experience and read it, but it is not the only action.

Your "actual" vs. "real" statement is equivalent to saying that dBB should drop the notion that the other books are not true. Just because they are in the library does not mean that they represent reality.

Your razor argument was aimed at the mathematical extra bit that dBB gives. I apply the razor to the set of stuff that the theory says happens. The unitary version says it is all true; infinitely many separate worlds which may "influence" us, but are not directly observable or able to be experienced. dBB says there is only one world and this is how it evolves.

Also, "the other points on the wavefunction" strike me as a wrong way to state it. The wavefunction is a function of the configurations. Those points are what they are. You can use the values of the wavefunction to decide the relevance of those points to existence, but it is part of the definition of the theory as to what is considered real or not. In dBB, there is one real configuration that changes in time being guided by a wavefunction that exists in some sense, but whose existence is only deduced from the motion of the particles. Saying more about it being really real beyond that is questionable; one simply says this is what the objects in the theory are and what they do with a clear mapping of what one needs to check in order to see if it corresponds to our experiments/experiences.

2. There is still the question of whether or not one can get a full theory that works without adding anything else. It can be done with just a little addition, say, adding a mass density formed by suitably integrating out positions. This makes it well-defined and one can do an analysis. It also gives 3-space a role.

This somewhat undercuts the razor since it is an extra thing though perhaps less of an effort than the trajectory equations.

To not have something additional is not something I have ever seen done in a convincing way.

a) The assertion is that a 3-space structure with particles moving around in that structure arises as an illusion even though nothing of the kind is actually happening in the theory. It should be appreciated that this is an extraordinary claim and one has to be super careful in doing an analysis to show that it happens.

The contrast with dBB is immediate. There are particles moving in 3-space. That's the starting point. By analyzing those motions, we see that there is some function guiding the particles and that function is a function on the set of all possible configurations. There is a natural and easy progression to see why our experience is the way it is. It is a very natural story.

In the unitary view, we are supposed to have this appearance of particles in 3-space in our experience, but that is not what actually exists in the theory. The only object in the theory is the wavefunction.

One might be able to argue that if one sets up operators based on 3-space and use that structure in generating the dynamics then we can read off the 3-space and particles, but ideally, one would be able to extract the illusion of 3-space (it is an illusion if the unitary dynamics is all there is) given the abstract Hilbert space and Hamiltonian. In some cases, such as free particles, it is provable that the base space cannot be extracted out uniquely to N particles in 3-space vs. one particle in 3N space.

Whether it can be done or not, it should be appreciated how straightforward the dBB theory is in contrast to the unitary dynamics.

b) Probabilities. What is it a probability of? That's the first question. If only the wavefunction exists and it is a unitary evolution, then there is no randomness, there is no probability. And the role of the unitary part of the unitary evolution becomes extremely obscure as well.

Moving on, pretending that the outcomes of experiments can be looked at in this theory and the history looked at, then we would want histories that give the right probabilities according to standard QM. But since all the outcomes are considered to happen, then there are histories with, say, the cat always ending up dead. One gets the wrong statistics in those "worlds". These may be thinly represented in some sense, but it is not clear from a purely unitary dynamics what that sense could mean. In terms of existence, they do exist and thus this theory predicts that wrong statistics definitely occur though our personal histories might not observe it.

c) Who are we? In a unitary dynamics viewpoint, what is an individual in this story? In dBB, it is roughly a collection of particles moving and shaped in roughly an individual way, more or less. It is not hard to see us. But in unitary dynamics, with constant spreading, more and more of us exist and spread out. So to even talk about my experience becomes rather outside of the theory.

d) Imagine a wavefunction that is non-zero everywhere on configuration space. Does that mean that everything, including the future and past of our own personal experience, is happening right now? It is not only saying that all of the histories in the Library of Babel are true, but every single page is happening simultaneously. This includes memories of eggs reassembling and all sorts of other strangeness. That is to say, predictive power seems to disappear entirely.

The free dynamics tend to spread out the wavefunction and thus either that spread out nature needs to be accepted and understood or one has to argue that the interactions are keeping it tightly confined.

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A good starting point with a theory is to say what one cares about in the theory getting right. For dBB, this is the position of the particles. Everything else is needed to understand and account for the observed motions.

In unitary wave dynamics, all we have is a single wavefunction that evolves. Why do we care about this; how do we model our experience with the wavefunction? That's the question that needs to be clearly and unambiguously answered.

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Locality. The wavefunction is a non-local kind of object. That is just what it is. That is where the non-locality of dBB comes from. Indeed, taking the wavefunction seriously is largely what many object to in dBB. Bell proved that nature has some kind of nonlocality assuming that experiments have results when we think they happen. That's the choice. Either deny experimental results or accept non-locality.