It will be impossible to do what you want with water waves, because water waves are in physical space, and the effects of collapse and measurement only show up when the waves are propagating in enormous dimensional configuration spaces. The way to get the quantum effects in systems like this is to restrict the mechanical motion to a few quanta, but for water waves the quantum is essentially zero compared to the thermal energy.
You can see the interference pattern just fine with water waves, the issue is when you measure the position of the "particle". The number of elementary quanta in a water wave, or any other macroscopic wave, is so enormous, that you can measure the wave amplitude without disturbing the wave at all. In order to see the breakdown of interference in response to measurement, you would need to have only a few oscillation quanta of the water surface waves, so that measuring where the water was waving would localize the wave by entangling it with the measuring detector, and lead the remaining relative state of the water to show no interference.
The point is that the measurement effects are not due to the wave nature of matter, but due to the entangling nature of quantum mechanics, where waves travel in configuration space, so that they are waves over different possible worlds, not over the position of separate single particles. Without this enormous configuration space wave, you don't get a model for the measurement issues.
This is impossible in water, because the thermal energy at temperatures where water is liquid is essnetially infinitely larger than the energy of a single quantum of water oscillation. Because of this, the notion of a single quantum of water wave is difficult to define, and might not make coherent sense. You can't have a single quantum, because the thermal noise at any realistic wavelength and temperature is much larger than the quantum of energy.
But you might be able to pull off a double slit experiment at ultra-low temperature using a phonon in a solid, or a fluid excitation in liquid He, which might satisfy the criteria you want.
I think the experiment you are proposing is not possible in the way you want it.
Let us say we produce two photons in an electron-positron-annihilation with total momentum zero. (Since I don't see an easy way to produce entangled electrons I will talk about photons here, but I think it is not important for the argument). Those two photons are of course entangled in momentum: if one has momentum $\vec p$ the other one has momentum $-\vec p$.
But in order to make this statement you have to make a moemntum measurement on the initial state, i.e. know that the total momentum is zero with a certain $\Delta p$. But then, by means of the uncertainty relation, you only know the position where the photons were emitted with an uncertainty $\Delta x \propto (\Delta p)^{-1}$.
Now you can have two scenarios:
Either your double-slit is small enough and far enough away that due to the uncertainties $\Delta p$ and $\Delta x$ you do not know through which slit your photon goes. Or you still can tell (with some certainty).
In the second case there will never be an interference pattern. So no need for entanglement to destroy it.
But in the first case, due to the uncertainty $\Delta x$, measuring the position (by determining which slit your photon takes) does not give you an answer about the entangled photons position that is certain enough to tell which slit it will go through. Therefore you will see interference on both sides.
So an EPR like measurement is not possible in the experimental setup you propose.
I would assume that in general you need commuting observables, like spin and position in the Stern-Gerlach experiment, in order to measure EPR. But I didn't think that through yet.
addendum, 03-19-2014:
Forget about the second photon for a while. The first photon starts in a position state which is a Gaussian distribution around $\vec x_0$ and a momentum state which is a Gaussian around $\vec p_0$. After some time $t$ its position has evolved into a Gaussian of $\mu$ times the width around $\vec x_0 + \vec p_0 t$ (mass set equal to 1) while the momentum state is now $1/\mu$ times the width around $\vec p_0$. So while your spatial superposition gets larger - and thus better to measure with a double slit - the superposition in the momentum state, in which you have entanglement, gets smaller. You don't gain anything from entanglement, since your momentum wave-function is so narrow, that you know the momentum anyways.
It is actually not important to have space and momentum for this. Just take any non-commuting observables A and B, say with eigenstates A+, A-, B+, B-, and take two states S1 and S2 that are entangled in A. So measuring S1 in A+ implies S2 in A- and vice versa. But what you want is measure if S1 is in B+ or B- and from this conclude if S2 is in B+ or B-. And since A and B do not commute, measuring B with some certainty gives you a high uncertainty on A, meaning, for knowing if S1 is in B+ or B- you completely loose the information if it is in A+ or A-. So you cannot say anything about S2. On the other hand, as long as you are still in an eigenstate of A and know what to expect for the A measurement of S2, you don't know anything about the result of the B measurement.
So in order to do an EPR experiment you need entanglement in the observable you measure or an observable that commutes with it.
Please tell me if my thoughts are wrong.
Best Answer
Great question! I suspect the reason you can't find videos (although I haven't looked for them myself) is because most of the videos of interference will be videos of photon interference, since that is the easiest kind of interference experiment to do. However, the only kind of measurements we can perform on photons in this experimental context are what we call "destructive" measurements: for example, you could just block off one of the two slits, and then for any of the photons that get through you will know which slit they went through... but you will be destroying the other half of the photons.
This is therefore not as compelling an illustration of the collapse of interference patterns as an experiment in which you can measure which slit the particles go through while still allowing them to pass through the slits. For this, you need to use some other kind of particles, such as electrons. This has been done, and the interference pattern indeed collapses when you measure which slit each electron passes through, but I still don't know if there is a video...