I realize that the online language guide offers a formal description, but I'd rather not attempt to scrape it off the webpage if I can simply find a more raw description.
The closest to what I want is contained in this document - which is too outdated to be of any practical use, unfortunately.
Unfortunately, I don't think there's a BNF version of the grammar in The Swift Programming Language. As you probably read already, the formal grammar there was written for people to read more than building a parser. There are a few places where it overproduces (the grammar matches invalid Swift code) because the stricter grammar would be really hard to follow — for example, it doesn't enforce which attributes are allowed on a particular kind of declaration.
If you have a minute, do you mind filing a bug against that document in Radar? It would be useful for us to know a little about what you're trying to do.