Good info, lanejudy. Over the years I've seen a lot of specials, generally for targeted groups such as military, pass holders, Florida residents, and other groups. Also, of course, they discount fares as a cruise date approaches and rooms remain unsold.
As for TA discounts, they do exist, they are just disguised as onboard credits, but they do lower your total cost. Generally I've seen these credits are inversely proportional to the quality of service...TAs who will only deal with you via email tend to offer more, and those who will talk with you and help you plan your cruise tend to offer less. Fair enough.
But, as for the (apparent) large discounts on other lines, I haven't seen Disney offer them for a while. We book as early as we can, and have always seen the price increase.