One suggestion I have here is to have at least two different sections of the UI. One part would be the actual document and the other would be the scratchpad. It seems like much of what you say would not actually make it into the document (edits, corrections, etc) so those would only be shown in the scratchpad. Once the editor has processed the text from the scratchpad then it can go into the document how it's supposed to. Having text immediately show up in the document as it's dictated is weird.
Your big challenge right now is just that STT is still relatively slow for this usecase. Time will be on your side in that regard as I'm sure you know.
Good luck! Voice is the future of a lot of the interactions we have with computers.