How to reconcile Kierkegaard's model of worship with Existential authenticity? I've been told Kierkegaard suggested that worship be a form of theater where the congregants are actors and pastors are directors.  (This is the only on-line reference I could find, does anyone have a link to a more authoritative source for this?)

Kierkegaard is regarded as an Existentialist.  Existentialists stress the importance of Authenticity.

Can someone please explain how it would be possible to worship authentically if a worshiper is merely acting?
You are misunderstanding the point being made in the article linked to. The 'drama' description is being used as an analogy to what people are doing in the worship service, not to whether they are 'pretending'.  In other words some people are 'directors' (telling others what to do) some are 'actors' (doing stuff) and some are 'audience' (watching stuff being done). When they talk about people being 'actors' they don't mean they have to pretend - it means they have to do stuff rather than just watch (that's the original meaning of the word actor - one who takes action).

The point being made on the web page, and presumably by Kierkegaard (though there isn't any reference to back it up), is that there are churches where the congregation are mere audience - watching what is happening without taking any part. He believes this is wrong, and that the congregation should take an active part in the worship. It doesn't mean they have to 'pretend'.