A.Stars says participial phrases are only adjectival, so they can't modify the verb.
In your new example, we have a "being" verb, so it has to modify "explorer." I know that sounds dumb, but when you say it describes what you're doing, that makes it sound adverbial.
Although I know it's a present participle, it has the feeling to me of a conjunction, like "and" or "as well as." (I realize "including" is logically different.) I can't get my brain around the idea that "including" by itself describes anything. I'd agree that the phrase "including bananas" describes "fruit." I don't know why it bothered me so much. Just a participial phrase functioning as an