>>37Tis meet that some more audience than a mother, since nature makes them partial, should o'erhear the speech.
This is plural: he's referring to mothers as a class. "...than a mother, since nature makes
mothers partial..."
There's not a man I meet but doth salute me / As if I were their well-acquainted friend
This is plural: he's referring to all the men he meets. This is obvious if you continue reading: "And every one doth call me by my name.
Some tender money to me; some invite me;". Some [men] tender money to him, some [men] invite him. Plural again.
And every one to rest themselves betake.
"Everyone" is obviously plural as it doesn't refer to a particular person but rather to a group.
If that's all the evidence you've got, then I can safely conclude that this "singular they" is an ill-begotten child of the past couple of decades.