With a pinch flat, shouldn't he have a "snakebite?"

The OP might look for another puncture nearby the first, so that the two punctures together look like a snakebite.

If the OP has a snakebite, I would recommend that at 288 lbs he inflate his rear tire to the maximum pressure printed on the side of the tire.

If the OP's tire doesn't allow more than 120 lbs per inch, he might consider a tire like the Schwalbe Ultremo that goes to 140 lbs and has very good flat resistance.

He might also consider a 25mm or 28mm tire, with the rear tire pumped to the max.