I agree that the 60,000 word estimate seems wildly high. Ever read the prose of “the average college student”? Me thinks Professor Crystal is using very suspect methodology. It simply fails the common sense test.
I think the issue you raised merits its own GQ thread. 
Actually, I’m not questioning whether the statement that the average college graduate has an active vocabulary of 60,000 words and a passive vocabulary of 75,000 words. That may or may not be true, but it’s not at all the same thing as it is to say that the number of words used in a person’s body of writings is a certain number. There are three different things to measure here.
The first is the person’s passive vocabulary, which is the number of words that they understand. To measure this, you could give the person a list of words picked randomly from a dictionary. Take the percentage of these words that the person knows the meaning of, and multiply this by the number of words in the dictionary.
The second is the number of words used in the person’s body of writings. Obviously, if this person hasn’t written anything, there’s nothing to measure here. If they have written something, go through the entire body of their writings and count the number of words they use.
The third is the person’s active vocabulary. This is harder to measure. You could have the person writes essays about some assigned subjects. Look through the essays for the most difficult words used. Use these words to estimate the number of words that this person could use if they wanted to.
Notice that the passive vocabulary is greater than the number of words used in the body of the person’s writings, which is greater than the active vocabulary.
Another consideration is that many of the historical documents and prose that evidence the evolution of the English language very likely do not reflect the “common tongue” of their representative era very accurately. As most people able to write during those times were uncommon and highly educated by the standards of the time, their prose was prone to a certain intellectual and flowery syntax and their writing style was probably impacted more by Latin and Romance languages than would actually be apparent in the spoken language of their contemporaries. These older Documents often reflect a specialized or formal language much more representative of the priveleged and intellectual minority.
Actually I was referring to the Mayflower quote; I thought Winthrop’s quote was fairly apt, actually. Nonetheless, Winthrop was fully capable of writing lengthy sentences, of which I will spare the reader.
Small piece of the puzzle:
I flipped through my copy of An American Primer, a collection of American documents edited by Daniel Boorstein. Mary Easty’s Petition of an Accused Witch (Salem: 1692) and Gabriel Thomas’ 1698 promotional tract An Account of Pennsylvania both abjured periods to one extent or another.
Benjamin Franklin (1757), in contrast, displayed a comparably modern penchant for shorter, crisper sentence structure. So perhaps a shift occurred during the first half of the 1700s.