There's some weird best fit algorithm going on here - if I try to book 12/30-1/4 there's PLENTY of rooms available (starting at $655 a night!) but as you go down to 12/30 - 1/3 then 12/30 - 1/2 the rooms drop off dramatically
It's definitely an algorithm but it's not anything weird. It's a practice known as Revenue Management and it's something done by virtually every hotel on the planet.
Without getting into too much detail, Revenue Management basically saves rooms for guest staying for multiple nights by instituting stay controls. The easiest stay control to understand is the minimum stay. The simplest example is Las Vegas.
Given the proximity of Las Vegas to the 23 million people living in Southern California, it's almost a given that all the major hotels will sell out every Saturday night far in advance. In order to maximize their revenue, hotels will require guests to stay 2 or 3 nights in order to make a reservation.
Without question, Revenue Management is good for hotels. But, it's also beneficial for any guest that stays more than one night. If Disney didn't use it, guests wanting a longer stay would have difficulty finding a room unless they book super-far in advance because Florida residents would theoretically grab most of the inventory on short weekend stays.
There are other more complex stay controls that are used. Additionally, many hotels use rate controls, as well. For example, if you book a multi-night stay, you might get a discount. But, someone staying 1 night might have to pay the full rate.
Note: I worked as a Revenue Manager in two different hotels. I also worked at the Disney Reservations Center in Orlando...but not in a role that directly involved Revenue Management.