How about thermoelectric cooler with a fan instead of just a fan, there's a palm sized one for cooling pc boards & chips. I dunno, put the big heat sink around the coil and somehow attach the cold side of the cooler to the heatsink so it can soak up the cold.

But I agree it's the single coil design. Only pin I ever had where the flippers would start weakening was LOTR and it really pissed me off. I think I put heatsinks on them but my memory fails me. My WPT didn't seem to weaken that I could notice though.

The one I googled is a self-contained unit with a fan that blows the hot air out the top. I think they are made for people to cool the back of their smartphones. The cold side is just a big metal plate so the issue would be sinking the plate to the coil, or to a heatsink on the coil. But no idea how much power one of these things would need in order to compare to a fan blowing on the coil, this size might be totally insufficient..

How much did it rise in the cabinet with the heatsinks vs. without?

I don't see it making much difference, the flipper is still putting out the same total amount of heat if you play it for 2 minutes or two hours. A fan on the coil is just distributing it faster thru the cabinet. It's not like playing the flippers as is for an hour isn't going to heat the cabinet up just as much on average.