This question is prompted by the earlier question Should I use a hyphen after -ly when modifying a verb in the past participle verb? Please don't close this as a dup unless there's a later answer there that answers my specific question (or another relevant question that I haven't been able to find).
My hypothesis is that adjectival "-ly adverb + past participle" combinations are more likely to include a hyphen when they occur before the relevant noun. But my Google-fu is inadequate to the task of establishing whether this is true or not, and my knowledge of formal grammar certainly isn't good enough to know of any "rules" that might be involved here.
Note the [optional] element in the example usage forming the question title. I don't see why...
Coffee boiled is coffee spoiled.
...should be grammatically any different to...
Coffee boiled is coffee which is spoiled.
...but I'm prepared to be disabused on that point.
Is the hyphen in my question title any more justified in the first badly written than the second?
EDIT: In case I haven't made myself clear, I'm not asking for answers telling me that the hyphen is never justified. Unless they're accompanied by evidence (not opinion) showing that in fact my hypothesis is untrue anyway, so it's meaningless to ask why the phenomenon occurs.