Do you know of any cases in which philosophers suggested ways of thinking about things which then got used productively?
Sure. Roger Bacon. Sir Francis Bacon.
Both of whom, I note, greatly respected Aristotle while deriding the "Aristotelian" philosophers of their days, which suggests the problem in the Galileo and Copernicus cases was less defects of Aristotle and more defects of Scholasticism (during Roger's day) and Second Scholasticism (during Francis's day).
I've often wished for a list of cases where philosophy has proven useful, or has at least anticipated science in drawing correct conclusions. Here's one for the list:
The June 18 2010 Science has two very similar articles on how rat brains represent space. Both conclude that the brain already represents space as a grid before rat pups take their first steps into the world. Both make the point that this validates Kant's claim that space is an innate concept prior to experience.
(The next task is to make a corresponding list of cases where philosophers made incorrect conclusions; and estimate whether the number of correct conclusions is greater than chance.)