New member here.
Quite a few years ago (maybe 15) I worked on a massive insurance claim made by a cruise company, for a number of cancelled sailings. One of my jobs was to determine the loss of revenue to the cruise company. As you can imagine, one of the 1st questions we asked was how much a passenger pays for their cruise. There was actually no set answer.
When we actually started to dig down into the figures, we could see that early bookers got an early discount, direct bookers got a direct booking discount. Bookers via a travel agent got a travel agent discount. And the late bookers also got a discount because the cruise was not fully booked. All the discounts varied slightly, but not by much. After spending a long time analysing the figures, we did not see any particular trend or indication as to the best way to get a significantly cheaper cruise.
Perhaps times have changed, and perhaps different cruise lines operate different pricing structures. But having since become a fan of cruises, even though I did a lot of work on those claims, I don't think that there is a magic answer that will end up saving you a huge amount of money.
One cruise company we use sometimes offer pretty good value last minute deals on under booked cruises - but they tend to be the shorter and less exotic voyages.