I researched this, and I believe the answer is that you cannot get the parsing directly from Parsey McParseface or any other syntax model.
Syntax analysis is fundamentally different from dependency analysis , and the syntax network is designed to create dependency analysis. In fact, the CoNLL format , which the syntax yields, is not even able to display the parsing tree:
The HEAD and DEPREL fields are used to encode the dependency tree above words.
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