As I have been saying, this date was solely for the purpose of focusing world attention on Iran as an Islamic religious authority. There was no surprise to wait for - the message was conveyed simply by the date itself, an Islamic holy day.
My theory is that they wanted to choose their own date rather than have it set for them. They did not want to appear to be responding to any deadline set by someone else, they want to control the agenda. The Islamic holy day was a logical choice for the reasons you state.