"They" isn't ambiguous at all, though it is occasionally clumsy. It is even (mostly) gramatically correct.
Certainly it works better than "this one" instead of "I."
As a complete aside, I've found I like how a few RPG manuals are handling the pronouns in their text. Instead of trying to use "they" (clumsy) or swapping pronouns every once and a while (confusing and distracting) they always refer to the GM as "she" and the player as "he," or the other way around.
It's actually helpful. You know who's being talked about even if you start in the middle of a paragraph, and remove some of the implicit assumption that females will never, ever play this game.
Our language would be better off to drop gendered pronouns, and instead go with numbered ones.
First actor, second actor, third actor, fourth actor, fifth actor.
Pri thought that Sec was talking to Ter, but Sec was really in communication with Qua, while Ter and Qui were in discussions.
I can't tell you the history of "they" as a singular pronoun, but I can tell you that my english professor this term was previously a professional editor and singular "they" is a pet peeve of his. Hence, I am avoiding the use of it for the season
In computing circles, where "One thought that Two was talking to Three, but Two was really...." would actually be appropriate, typically the abstract classes are instantiated like so: "Alice thought that Bob was talking to Charlie, but Bob was really..."