If you try to upload a 4K movie directly from Photos in iOS, it automatically drops down the quality to standard definition. To get around this, you just need to use iMovie instead.
For whatever reason, the native iOS YouTube uploader will allow you to upload 720p and 1080p videos to YouTube without a problem, but when you try to upload a 4k video, it only gives you the "standard definition" option. Gawker's own Shep McAllister pointed out to me that the best workaround for this is to just use iMovie to upload the video. After you record a video, just load it up in iMovie, select the upload to YouTube option, and you're all set. It's a silly workaround, but it does the trick. You can always just share the video to your computer and upload from there, but this is a nice way to do it straight from iOS.