It looks like the answer is no.
The second DocumentGroup is necessary for opening a file of the second type, but I haven't found a way to make SwiftUI create a document of that type. Using .handlesExternalEvents doesn't seem to help, as it seems to want to open a window defined by a WindowGroup rather than a DocumentGroup.
The best idea I've come up with is to create a temporary file and then push the URL for that to openURL, but that leaves the user with a file which they don't actually need, and doesn't replicate the experience of a new document.