No worries. This might be specific to my computer. It's odd, as even when I am in the pixel-perfect center of the object with the label "BOARD" above it and press "E" early in the loop (which I believe one of the initial sheriff dialog options tells me to do), nothing seems to happen.
EDIT: With the help of a macro that spams the E key, I was able to beat the game. Definitely an interesting concept, taking advantage of information so that the 15 seconds are enough. I'd be interested to see how this concept could be expanded upon. (slight SPOILER alert: I can imagine a trickier puzzle that could be added that would require you to use multiple echos in a single loop to get all the materials you need, although such a puzzle could be frustrating if you fail the maneuver and have to do the whole setup again.)