I think it would be totally fair not to allow the creator of the post to make edits or have the ability to delete their posts once the OP of the self-moderated thread has removed them. Just like how when a post is deleted by a moderator we completely lose access to it, it should be the same in this case, because once the OP deletes your post, it goes into the reserve and can only be seen, but nothing can be done to it.
What if the OP has some adjustments to make on the thread he created and isn't allowed to make edits or some adjustments would Op has to re-post in that same thread or what? Usually, the op should be permitted to make adjustments on their own thread but as we know whatever that is posted on any thread/topic is automatically archived so, even if they edit it for their personal interest or gains it can be still be revisited to know the original content op posted or even the deleted from the thread.
Usually why I do not so much like a self-moderated thread because is just for personal gain where the original creator has the ability to permit any post that would be posted there or not, but for topics that are related with finance or transactions I wouldn't encourage that to be self-moderated except for a special cases where the creator is either a staff or reputable member on the forum with much trust rating than a newbie or Jr member.