That is a really excellent question! It goes straight to the heart of what is actually going on. I give a longer explanation of this in the last section of my paper, but here is the TL;DR: The way in which you get copyable classical information out of non-copyable quantum information is by discarding parts of the wave function. The mathematical description of this operation is called a trace. The classical information that comprises our classical reality is a proper subset of the quantum information in the universal wave function.

The next question people usually ask at this point is: isn't that just multiple-worlds? And the answer is: yes, it sort of is, but with one important difference: the MWI insists that all of the myriad multiple worlds are equally real. And if you take the "god's-eye point of view" and look at the universal wave function, this is true. But it is not possible to actually take the gods-eye view except in the abstract. In order to take any "point of view" at all, you have to be a classical entity. So nothing can actually take the god's-eye view, not even God! Only a classical entity can take a point of view, and that point of view is necessary bound to one particular universe, and so that universe -- your universe, and mine -- is privileged from our mortal's-eye point of view, which is the only point of view anything can ever actually take.

I feel like the question has not been fully answered. After taking the trace, how do you make enough information-copies to tell all your friends about it?

The trace is just the mathematical description of how you get from quantum to classical. The TL;DR is that a proper subset of a quantum system behaves, when considered separately from the rest of the system, as if it were a classical system even though it really isn't. To see the details, read this:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.79...

For some additional background:

https://adami.natsci.msu.edu/blog/2014/6/26/on-quantum-measu...

Just to be clear where I'm coming from, I have taken a course on quantum information theory, so I'm not completely lost here. But some things I for-got and somethings I never-got.

And in particular, the (separate) course on qft lost me at hello, so I never got the chance to incorporate that into my worldview.

In that case: if you look at an entire macroscopic system, isolated from everything else, before and after a measurement, you will find that the total entropy of the system has not changed. It can't because the evolution of an isolated system is always unitary.

If you trace over any degree of freedom of the system (i.e. separate the system into two parts, which are usually the "particle being measured" and everything else) then what you will find is that after the measurement the degree of freedom over which you traced has a negative entropy, and the rest of the system now has a positive entropy (which is the source of the apparent randomness), and that all of the degrees of freedom of the rest of the system (in the preferred basis as determined by decoherence) are now in classical correlation with each other. That is how you make "copies" of (classical) information.

Thanks for the pointers, I'll have to think about this!