I think your analysis is a good one. But you could also say the sentence is eliptical, and speaking modifies I , or one ,or you . Broadly speaking, [ one/I/you could say that] the project was successful.
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AnonymousWell, I have another idea.
I think "Broadly speaking" is an adverbial phrase modifying successful. It tells how successful. project / was < successful
Sounds good to me! So you could substitute something like, "In general terms," and your analysis wound be the same? In other words, it's irrelevant that "speaking" is a present participle an