OK I got hold of the paper, which is a very nice read, I can email it to you if you want. It's from a talk David Deutsch gave at some conference, I bet he is a very entertaining speaker. My summary won't do it justice, but anyway. The experiments are the following:

Experiment 1:

Measure the current time and call it t1. Note that you are conscious at the time you are observing the value t1. Wait. Check your watch again. It is showing a different time t2 now. You are still conscious and your consciousness is in a different state than at t1. Therefore you've detected experimentally a superposition of distinct states of human consciousness, since there exists a formulation of Quantum Mechanics in which time is a regular operator like any other observable and you've observed two different values of it.

Experiment 2:

Consider a computer which is so well isolated that interference can be observed between it's computational states. The computer is programmed to perform an algorithm which takes one bit of input, and produces one bit of output. The algorithm is very computationally expensive and takes a long time T to complete. We communicate with the computer via two observables, I (for input) and O (for output).

Prepare the initial state as a superposition of both input values 1/sqrt(2) * (|I=0> + |I=1>). After the time T, the computer will be in the state 1/sqrt(2) (|I=0,O=f(0)> + |I=1,O=f(1)>), where f(n) is the output the algorithm produces for the input n. So by measuring I and O at this point we will either learn the value f(0) or f(1), but not both. But say we are really interested in f(0) XOR f(1). Classically, it's impossible to calculate it without computing both f(0) and f(1) so it has to take the time 2T. But with our computer, which is in a quantum superposition of states, and with the help of some clever algebra, we can construct another observable R. When we measure R one of the two things happen with equal probabilities: either we get the correct value of f(0) XOR f(1), or we lose any hope of learning it from our system. We know which one happened, i.e., with probability 0.5 we will have the correct value for f(0) XOR f(1) and we will know for sure it is correct.

Since we obtained f(0) XOR f(1) in half the time, clearly there existed two parallel worlds in which two versions of the computer calculated f(0) and f(1).

(It is noted that some members of the audience objected that Experiment 2 is conceptually no different from the two-slit interference experiment. The author allows that this may be so in a sense, since indeed, the two-slit experiment alone should be enough to make it obvious that the Everett's interpretation is right, however Experiment 2 makes it even more obvious.)

Experiment 3 (simplified version):

Consider a system consisting of a spin 1/2 particle and a quantum computer running a simulation of human consciousness. Prepare the spin in the state |→> = 1/sqrt(2) (|↑>+|↓>), i.e., measuring the spin along the x axis will always show it's pointing to the right, which means that measuring the spin along the z axis may give up or down with equal probabilities. Have the conscious being in the computer measure the spin along the z axis and communicate to the outside world the fact that he/she observed one of the values 'up' or 'down' (without saying which one). Then undo all the transitions the combined system underwent, i.e., revert it to the original state (which is in principle possible for a system consisting of a quantum computer and a microscopic system). Then measure the spin of the particle along the x axis. If it shows 'right' every time (we need to repeat the whole procedure many times), then the Everett interpretation must be true, since otherwise the fact that a conscious being observed 'up' or 'down' would have caused the particle to collapse to a state in which 'left' and 'right' are equally likely.

(The original formulation of Experiment 3 was more complicated, with three spins not one and some more clever algebra, the purpose of which if I understand correctly is to prove that it's possible to communicate to the outside world the fact that a measurement along z axis was taken, without losing the ability to revert the system to the original state.)

So, there. I'll let you form your own judgement.

Counter to your previous assertion, we could in theory experimentally determine whether this is true via trained rats: (1) Train a rat to perform measurements, (2) kill the rat before it has a chance to tell you the results, (3) check to see whether wave function has collapsed.

It doesn't work that way, because even if the rat doesn't cause the wave function to collapse, it interacts with the system and causes a transition, from the original state to a state which is a superposition of states corresponding to various values the rat might have gotten from the measurement, each of these states individually looking exactly as if the rat collapsed the wave function, with the coefficients such that the probabilities for each value come out right. And killing the rat afterwards does not undo it. So you will observe that the wave function has collapsed. Same if you use a mechanical detector in place of a rat.