Hello Éva!
You have stumbled upon a really nice challenge there :)
I looked at it, and what I found is that the message must be generated during one of before-store/after-store stages. So, unless you are willing to try injecting another message via Code Pack (30€), you might eventually try something in /layouts/joomla/system/message.php where the message is generated, for example test if the user is logged in, and if not, than probably is submitting a new registration so you can "inject" your new reg. message, or else the edited reg message. On a side note, the message does obey the JText conversion, if that brings any ideas.
My suggestion would be to create 2 Free Text message fields with your messages above the Submit button, and by using Conditional States (Site Form | display mode #5) you can display one message or the other based on if user_id Is Empty condition. Naturally, user_id must be present in the form, but you can put it into HIDDEN position or hide it otherwise.