OK, here are my further thoughts on all of this. Put very simply, regular English adjectives and adverbs form their comparatives and superlatives by inflection (-er and -est) when they are short and by a phrase (more . . ., most . . . ) when they are long. Adjectives that end in -ing, as they do when they are formed from a verb, take phrasal comparison, so amazing, for example, becomes more amazing and most amazing. That allows us to say things like the most amazing sight.
Adjectives in -ing, like all adjectives, may be modified by an adverb. In a working man, the adjective working can be modified by the adverb hard. How should we write the result? A hard working man could be construed as a man who both works and is hard, which is not the meaning intended. A hyphen gets us round the difficulty: a hard-working man. What if this paragon is exceptional, a harder worker than anyone else? No problem. We can call him the hardest-working man. Comparable examples might be the fastest-boiling kettle on the market, the longest-running show in London, the slowest-moving traffic.
How does this translate to the OP’s examples? Fastest-drinking college student and quietest-singing bird are on the same pattern as hardest-working man. In both cases, the word that modifies the -ing adjective is a superlative adverb. That is not the case with the unfortunate most burping woman. There, the words most burping form a superlative adjective on the same pattern as most amazing and, as Gwanme has shown, no hyphen is required. Highest-grossing film gets a hyphen because it’s on the same pattern as hardest-working man: grossing is an adjective modified by the superlative adverb highest.