To muddy the waters, I'd find this super duper weird. I've never had a chain of texts end with a formal "close" to the conversation. Doubly so since texting is

To muddy the waters, I'd find this super duper weird. I've never had a chain of texts end with a formal "close" to the conversation. Doubly so since texting is async. I'd finally look at your "I have to go" message hours after you sent it and be confused at the update.