How do you get an ensemble with Copenhagen and only one universe?
You do the same experiment many times.
This is ranging too far afield- lets refocus. I've said my piece, and linked to the literature. If anyone has questions about the literature or is looking for more information, let me know. Otherwise, I'm going to drop this line of argument. People who argue the number of universes is uncountable should ask themselves what it would mean that results of experiments are uncountable. If they have a satisfactory answer (and one that leads to Born probabilities) they should publish it. Repeating the same arguments over and over is not helpful or instructive. Also, if you believe in many worlds, but have never proved Gleason's theorem, I recommend you try. Its fun and instructive. I further recommend trying to lay down an axiom for your preferred method to get Born into many worlds and see where it leads. Also fun and instructive.
So lets look at a philosophical aspect, and Occam's razor. We'll ignore the technical issues with many worlds for the time being. Quantum mechanics is a response to two stylized facts (to borrow a term from the economists)-
1. there are classes of experiment where we can't predict the outcome
2. doing many of those experiments we can always predict the distribution
Rephrased in terms of observables-
1. certain observables do not evolve 'nicely'
2. the observable's expectation values do.
If we send one photon through two slits, no idea where on the screen it hits. Send a million, and we know what the distribution looks like.
The minimal interpretation, then, is to say that the wavefunction ultimately represents the ensemble of experiments, not a single experiment. What it actually predicts are distributions- after all thats what behaves deterministically! The wavefunction never 'collapses', it just never makes predictions about single systems. When we do a single experiment, we take one sample from the predicted distribution.
Now, what the many worlds advocates say is- no the wavefunction doesn't represent a distribution of experiments! It represents each single experiment! It LOOKS like a distribution, but thats because each experiment creates a distribution of WORLDS- but all of them exist. It sure looks like they are introducing a whole lot extraneous 'worlds' in order to deny empirical fact 1. They want to say that the ability to predict distributions somehow implies the ability to predict single experiments, as long as you can add as many extra worlds as you need.
This looks to me like a pretty severe violation of Occam, but to each their own.