2. Say the "crew were," treating the collective noun as plural, as we do with "couple."
3. Let it stand.
If you were an AP Stylebook strict constructionist (and if you are, why are you here?), you would say, "Nouns that denote a unit take singular verbs and pronouns: class, committee, crowd, family, group, herd, jury, orchestra, team."
That follows typical American usage; British usage prefers to treat such collective nouns as plurals, including saying, "Her Majesty's government were. …" And AP acknowledges some exceptions. Names of athletic teams, for one, are plural even when singular in form, as in the AP's example: "The Miami Heat are battling for third place."
Garner's Modern English Usage takes a more nuanced approach, expanding on the entry on nouns in the Chicago Manual of Style. Under the collective nouns entry, Mr. Garner writes, "Collective nouns sometimes take a singular verb and sometimes a plural one. The trend in AmE is to regard the collective noun as a unit: hence, the singular is the usual form. When the individuals in the collective or group receive the emphasis, the plural verb is acceptable."
We see this in the way we treat couple as either singular or plural, singular when the two people are considered as a unit—The couple is going to Paris on a honeymoon—and plural when they are considered separate individuals—on returning from Paris, the couple went their separate ways.
In Professor Cloud's example, many editors would chose No. 1, treating the members of the crew as a unit. Some would be receptive to No. 2, particularly if the sense were that the several members of the crew were coming from different places, not as a group. Those who follow Mr. Garner's advice, that "switching back and forth between a singular and a plural verb is lamentably common," would find that plural they after the crew was jarring and would reject No. 3.
But if Professor Cloud had not singled that sentence out for attention, I would likely have read over it without remark. Yes, in American English we typically treat collective nouns for groups of people as a singular unit: The United States Senate is an assembly of gasbags. But when we think of groups, particularly small ones, like a flight crew, as individuals, we are reluctant to use the neuter singular its and are willing to accept notional agreement.*
Notional agreement is more common in conversational writing than in the most formal writing, but as journalism aspires to be conversational, notional agreement will be indulged.
NOTE: Bill, I wrote a headline with they and a singular verb just to mess with you.
*Notional agreement, notional concord in Merriam-Webster's Dictionary of English Usage: "agreement of a verb with its subject or a pronoun with its antecedent in accordance with the notion of number rather than with the presence of an overt grammatical marker for that notion … agreement based on meaning rather than form." MSDEU notes that a plural pronoun with a singular noun as an antecedent is one of the most common examples of such concord.