In the Elitzur-Vaidman bomb test, information about whether the bomb has exploded does not feed into the experiment at any point. When you shoot photons through the interferometer, you are not directly testing whether the bomb would explode or has exploded elsewhere in the multiverse; you are testing whether the sensitive photon detector in the bomb trigger works.

As wnoise said, to directly gather information from a possible history, the history has to end in a physical configuration identical to the one it is being compared with. The two histories represent two paths through the multiverse, if you wish, with a separate flow of quantum amplitude along each path in configuration space, and then the flows combine and add when the histories recombine by converging on the same configuration.

In the case of an exploded bomb, this means that for a history in which the bomb explodes to interfere with a history in which the bomb does not explode, the bomb has to reassemble somehow! And in a way which does not leave any other physical traces of the bomb having exploded.

In the case of your automated blood glucose meter coupled to a quantum switch, for the history where the reading occurs to interfere with the history where the reading does not occur, the reading and all its physical effects must similarly be completely undone. Which is going to be a problem since the needle pricked flesh and a pain signal was probably conveyed to the subject's brain, creating a memory trace. You said something about "briefly freezing a small component of blood and skin on a live person", so maybe you appreciate this need for total reversibility.

In the case of counterfactual measurements which have actually been performed, very simple quantum systems were involved, simple enough that the reversibility, or the maintenance of quantum coherence, was in fact possible.

However, I totally grant you that the much more difficult macro-superpositions appear to be possible in principle, and that this does pose a challenge for single-world interpretations of quantum theory. They need to either have a single-world explanation for where the counterfactual information comes from, or an explanation as to why the macro-superpositions are not possible even in principle.

Such explanations do in fact exist. I'll show how it works again using the Elitzur-Vaidman bomb test.

The bomb test uses destructive interference as its test pattern. Destructive interference is seen in the dark zones in the double slit experiment. Those are the regions where (in a sum-over-histories perspective) there are two ways to get there (through one slit, through the other slit), but the amplitudes for the two ways cancel, so the net probability is zero. The E-V bomb-testing apparatus contains a beam splitter, a "beam recombiner", and two detectors. It is set up so that when the beam proceeds unimpeded through the apparatus, there is total destructive interference between the two pathways leading to one of the detectors, so the particles are only ever observed to arrive at the other detector. But if you place an object capable of interacting with the particle in one of the paths, that will modify the portion of the wavefunction traveling along that path (part of the wavefunction will be absorbed by the object), the destructive interference at the end will only be partial, and so particles will sometimes be observed to arrive at that detector.

The many-worlds explanation is that when the object is there, it creates a new subset of worlds where the particle is absorbed en route, this disturbs the balance between worlds, and so now there are some worlds where the particle makes it to the formerly forbidden detector.

Now consider John Cramer's transactional interpretation. This interpretation is all about self-consistent standing waves connecting past and future, via a transaction, a handshake across time, between "advanced" and "retarded" electromagnetic potentials (in the case of light). It's like the Novikov self-consistency principle for wormhole histories; events arrange themselves so as to avoid paradox because logically they have to. That's how I understand Cramer's idea.

So, in the transactional framework, how do we explain the E-V bomb test? The apparatus, the experimental setup, defines the boundary conditions for the standing waves. When we have the interferometer with both pathways unimpeded (or with a "dud bomb", which means that the photon detector in its trigger isn't working, which means the photon passes right through it), the only self-consistent outcome is the one where the photon makes it to the detector experiencing constructive interference. But when there is an object in one pathway capable of absorbing a photon, we have three self-consistent outcomes: photon goes to one detector, photon goes to other detector, photon is absorbed by the object (which then explodes if it's an E-V bomb, but that outcome is not part of the transaction, it's an external causal consequence).

In general, the transactional interpretation explains counterfactual measurement or counterfactual computation through the constraint of self-consistency. The presence of causal chains moving in opposite temporal directions in a single history produces correlations and constraints which are nonlocal in space and time. By modulating the boundary conditions we are exploring logical possibilities, and that is how we probe counterfactual realities.

A completely different sort of explanation would be offered by an objective collapse theory like Penrose's. Here, the prediction simply is that such macro-superpositions do not exist. By the way, in Penrose's case, he is not just arbitrarily stipulating that macro-superpositions do not happen. He was led to this position by a quantum-gravity argument that superpositions of significantly different geometries are dynamically undefined. In general relativity, the rate of passage of time is internal to the geometry, but to evolve a superposition of geometries would require some calibration of one geometry's time against the other. Penrose argued that there was no natural way to do this and suggested that this is when wavefunction collapse occurs. I doubt that the argument holds up in string theory, but anyway, for argument's sake let's consider how a theory like this analyzes the E-V bomb-testing experiment. The critical observation is that it's only the photon detector in the bomb trigger which matters for the experiment, not the whole bomb; and even then, it's not the whole photon detector, but just that particular combination of atoms and electrons which interacts with the photon. So the superposition required for the experiment to work is not macro at all, it's micro but it's coupled to macro devices.

This is a really good case study for quantum interpretation; I had to engage in quite a bit of thought and research to analyze it even this much. But the single-world schools of thought are not bereft of explanations even here.