Ok, interesting discussion. I'm going to be the heretic and suggest BOTH sets of numbers in the POH are correct!
NOT an aeronautical engineer, but here's my reasoning:
To state the obvious, it's excess horsepower over what is required to maintain level flight that allows the plane to climb. The IAS numbers that are decreasing are with the aircraft DIRTY, whereas the constant IAS figures are with a CLEAN configuration. My reasoning is that a lot of horsepower is being used to overcome the drag of the flaps and, especially, the gear. Drag depends linearly on the co-efficient of drag (Cd) but increases with the square of airspeed. I suspect the Cd of the gear is HUGE, compared to the Cd of a clean airframe alone. Thus, since you are already losing horsepower at higher density altitudes you don't want to waste all of it overcoming the drag of the gear, so a SLOWER IAS actually results in more 'leftover' horsepower for climb.
To put it another way, if you tried to climb at 82 mph IAS when 'dirty' at high DA you might be using all the horsepower to overcome gear drag and would barely be climbing.
Probably something flawed with my 'logic' here....Blast away!