The answer came from a member of the Clojurian Slack community: To pass an array to an annotation, just pass the value as a vector. I.e., look in the example from this doc for annotation SupportedOptions:

javax.annotation.processing.SupportedOptions ["foo" "bar" "baz"]

Also, for anyone running into something like this, remember @amalloy's suggestion to look at the compiled interface using java -v -p.