Here’s what I make of it:“To hear” is the qualifying infinitive that does the work of an adverb. The MC should therefore include “to hear”. “That all the members of the board complained …” is the (subordinate) noun clause and “that the new executive was difficult to work with” is another (subordinate) noun clause within the first subordinate clause. The two noun clauses are as you indicated direct objects of the verbs “to hear” & “complained” respectively. “To work” is similar to “to hear” is also a qualifying infinitive that does the work of an adverb.
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