Booking early gives you zero percent better chance of getting a discount. You still have to call first thing when the promo is released. If it's not showing availability for your resort or room type, then you can't get it without changing your entire reservation. So what's the advantage?
I've been recommending in all my articles, blogs, and posts that people should avoid doing this if they are booking to get a discount. It gives you no advantage whatsoever over someone calling for a new reservation that morning.
In fact, during the last
free dining release, the website opened up at midnight but the phones didn't open until 7am. Since you can't modify online, everyone who had a reservation had to wait 7 hours past everyone else...and essentially got last dibs. Everyone booking a new reservation had an advantage over those who already had one.
So wait to book, you'll be far better off.