This seems like a more complicated explanation than the data supports. It seems simpler, and equally justified, to say that praising effort leads to more effort, which is a good thing on tasks where more effort yields greater success.

I would be interested to see a variation on this study where the second-round problems were engineered to require breaking of established first-round mental sets in order to solve them. What effect does praising effort after the first round have in this case?

Perhaps it leads to more effort, which may be counterproductive for those sorts of problems, and thereby lead to less success than emphasizing intelligence. Or, perhaps not. I'm not making a confident prediction here, but I'd consider a praising-effort-yields-greater-success result more surprising (and thus more informative) in that scenario than the original one.