Update: I spent some time on this today, and y'all were right, the problem was a simple one. Orifice was blocked. There were flakes of some kind everywhere. It looked to me like the remnants of corrosion inhibitor from the internals of the unit. My theory is that the dealer-prep operations were the first time it had seen real hot temps, and that caused the coating to loosen. Then during transit in the following week, the stuff flaked off. Anyway, a bit of compressed air cleaned the burner, tube, and orifice right up and also knocked loose a good bit from places that couldn't be seen. I looked at the spark gap, and it seemed about right. I put gas back on it, flipped the switch, and it fired up on the first try.
Bottom line: water is hot, and you guys are cool. Thanks for all the input!