I finally figured out how to do this.
I just wanted to mention beforehand that I did try to start with a fresh Eclipse install, export the preferences to a .epf file, change just one single setting, export again, and compare the files. To my surprise, trying to import settings from a minimal .epf file did not work reliably either.
The solution that worked for me was to copy these files: {Eclipse workspace directory}/.metadata/.plugins/org.eclipse.core.runtime/.settings/*.prefs
I tried a fresh Eclipse install on another machine and after copying those files over, all my settings were restored perfectly.