> those 7-number participants simply felt that they worked harder and therefore deserved a better prize.

That is exactly how you expect reduced willpower to play out in practice in a situation where people are forced to make a conscious choice (as opposed to just absent-mindedly picking something). Nobody "just" takes the option that is counter to their long term goals, they rationalise the choice either then and there or afterwards, and rationalisations that we "deserve" something or are morally justified are amongst the easiest for us to grab onto.