Unfortunately ati doesn't have quite the wealth of tools that -intel does for debugging. What it does have is in the radeontools package. radeontool can be used for r5xx and older cards, and avivotool for r6xx and newer. Those tools essentially give you a GPU dump. I don't know if that's sufficient to debug these issues, but if you collect a GPU dump when it's frozen, and then again when it is not frozen, and include both files, sometimes those give clues.
Unfortunately ati doesn't have quite the wealth of tools that -intel does for debugging. What it does have is in the radeontools package. radeontool can be used for r5xx and older cards, and avivotool for r6xx and newer. Those tools essentially give you a GPU dump. I don't know if that's sufficient to debug these issues, but if you collect a GPU dump when it's frozen, and then again when it is not frozen, and include both files, sometimes those give clues.