Theme's 404 can't be exported (because it returns a 404?)

We have a custom 404 page. As with most WordPress installs, it's available at /404/ and returns a `404` when served.

So... WP2Static thinks it's failed and skips it:

Can anyone think of a way around this? I guess we could point the S3 error doc at another normal page, and make sure it returns a `404` status from S3.