In a passage in my English textbook I came across a sentence: “Two thousand e-mails would zoom his way within a few days”. I am wondering whether the blued italicized phrase (his way) in the sentence should be “their ways” since the subject of the relevant predicate verb “zoom” is “two thousand e-mails”. I am also wondering who/what the dependent possessive pronoun (his/their/its,whichever it should/might be) which is immediately behind the verb “zoom” refers to.

The following sentences are the context of the sentence in question:

…Soon the world would hear of Zewail’s award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom his way within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues…

Your help would be appreciated!
His way is correct. His refers to Zewail (who I presume is a single individual). The verb and the number of emails is irrelevant.
Thank you so much, Mister Micawber!