I am new to hunting there too, but the later is better cannot be true. If you go to the Alabama DNR website you can see all the kill number for each hunt for at least last year, and I think the last two years.
If you look at those numbers the most deer by far were killed on the very first gun hunt, then they drop off drastically each hunt.
You have a point, but when I looked at the data, it only shows the harvest on November 20, 26 & 27 in 2011. I wasn't able to find any data on December hunter harvest