Indeed, one can predict that problems with finding evidence for begin V NP will occur on the basis of Gricean principles of language production, where the heuristic be brief (which is part of the maxim of manner) will compel speakers to utter begin coffee as opposed to begin V coffee if V is one of the plausible interpretations of begin coffee.
on the basis of this Gricean reasoning, one might expect metonymies like (7a) and (8a) to occur with greater frequencies than their respective paraphrases (see (7b) and (8b)).