refrigerated air driers?

Agree. While not quite the same setup as you're talking about, I went with the same concept. I have an Ingersoll-Rand refrigerated dryer that I haven't connected yet, but it will be integrated here, at the yellow circle. Between the aftercooler and filter.
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I don't think you are going to see a big drop in temp across that cooler, so it won't pull much water out. It needs to be in between the pump and the tank to really be effective.