quantum mechanics - EPR-type experiments and faster-than-light communication using interference effects as signaling mechanism

I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse the wave function on the other side, such that interference effects would disappear? Making measurements on "bunches" of entangled particles would thus allow FTL communication, by making observed interference effects appear or disappear. How does such an experiment not:

1) Clearly imply that faster-than-light communication is possible?

or

2) (if #1 is rejected) Imply that measurement of one half of an entangled pair does not cause the collapse of the other half's wave function.

Why doesn't this thought experiment clearly show that if we maintain that FTL communication is ruled out, we must also rule out "universal collapse" in the Copenhagen interpretation?

EDIT: Here is an example of an explicit experiment (though I think experts could come up with something better):

You can entangle a photon with an electron such that the angle of the photon is correlated with the electron's position at each slit of a double slit experiment. If the photon is detected (it's outgoing angle measured), then which-path information is known, and there is no interference. If the photon is not detected, the interference remains.

The experiment is designed such that the photon and electron go in roughly opposite directions, apart from the tiny deflection which gives which-path information. You set up a series of photon detectors 100 ly away on one side, and your double slit experiment 100 ly away in the opposite direction. Now you produce the entangled pairs in bunches, say of 100 entangled pairs, each coming every millisecond, with a muon coming between each bunch to serve as a separator.

Then the idea is that someone at the photon detector side can send information to someone watching the double-slit experiment, by selectively detecting all of the photons in some bunches, but not in others. If all of the photons are detected for one bunch, then the corresponding electron bunch 200 ly away should show no interference effects. If all of the photons are not detected for one bunch, then the corresponding electron bunch 200 ly away would show the usual double-slit interference effects (say on a phosphorus screen). (Note that this does not require combining information from the photon-detector-side with the electron-double-slit side in order to get the interference effects. The interference effects would visibly show up as the electron blips populate the phosphorus screen, as is usual in a double-slit experiment when which-path information is not measured.)

In such a way the person at the photon detectors can send '1's and '0's depending on whether they measure the photons in a given bunch. Suppose they send 'SOS' in Morse code. This requires 9 bunches, and so this will take 900 milliseconds, which is less than 200 years. The point is that such an experiment would only work if you assume that the measurement of the photon really does collapse the wave function nonlocally.

Answer

I'm going to go ahead and answer my own question. I think the issue is that in my proposed experiment there would never be any possibility of observing an interference pattern without first destroying the entanglement that would allow (by measurement of the photon bunches) the switching on or off of the interference on the electron side. The entanglement between the electron and photon implies that there would be no interference pattern, regardless of whether or not the photons are observed. The only way to re-introduce interference would be to, for example, have the electrons go through a small slit prior to the double slit in order to spread their wave function. But doing this entangles the electron with the screen with the first slit in it and effectively erases its entanglement with the photon, unless the momentum of the screen with the first slit can be measured to sufficient accuracy after the electron passes through it. But interference will only be seen if the momentum of the screen cannot be measured to sufficient accuracy without compromising the corresponding uncertainty in the screen's position. Assuming that the level of this uncertainty cannot be controlled at will, the appearance of interference cannot be turned on and off by a distant photon/screen measurer.