Drafts is just using the OS dictation behind the scenes, so I don’t think there is an easy way. It’s more about dictating at that moment rather than piping in a feed. I think the Mac beta app at the moment probably isn’t using any workaround like the iOS version (which is probably the MacStories) reference, but I’m nit using the Mac beta currently so I may be wrong. If it does, then at that point AudioHijack might be able to pipe the playback of an audio file into the microphone input for the system and allow you to transcribe using Siri dictation for an extended period.
As an alternative, what about uploading your audio to YouTube as a private video, and then using the automated transcription from that? Might that work for you?
If you had two devices you could record audio on one and dictate into the other. I’ve not tried this but I have an iPad and an iPhone so could probably make that work.