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In the Quantum Eraser experiment, I understand that the particles are arriving at the screen before they arrive at the detectors or information eraser.

What would happen if we could increase this delay to something like a few seconds (I can think of a handful of ways to slow this down). Then we could take a photo of the interference pattern on the screen before the information is stored in the detectors. Once the information makes it to the detectors (if we observe it before it gets erased)...would the photo that we took change to show two beams? Has this been done?

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Your experiment will give absolutely the same result. Contrary to the impression you may get from the popular literature all this entanglement stuff appears only in correlations. So you will get a pile of data corresponding to the same pattern as usual of two lumps combined behind the slits, you will later get another pile of data for the other particle. And when you after everything is measured select from the first pile those instances when in the second pile you've got some particular result you may get the interference pattern. Please read this and this answers

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