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Are you still comfortable with this explanation if the photons are released with a 1-second gap between them and the tally is visibly shown building up into the interference effect on a computer screen? "Interfering with each other at an enormous rate" might mislead you a bit; neither "each other" nor "enormous rate" is particularly important in the double-slit interference pattern.

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Actually, you can't know this until you get a lot of measurements to see the pattern. E.g. if you just put one photon through you get one dot, and you'd be hard pressed to infer anything from that. So in the end you still need a lot of measurements to detect interference.

Also I bet you could mess with the interference pattern by pulsing the light source. This would be the lesser known form of the Uncertainty principle, where energy and time are unknowable.

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