I thought I remember the season closing on May 26th one year, not sure though.
With the season closing the 21st this year, that is the earliest closing date I can remember.
Since I am a non-res I have always hunted 6th season.
There was a time (before they went to 7 zones) that I could only draw 6th season and no extra tags! Actually there were years I couldn't even draw a tag.