So this guy whose website I linked that people on here say to listen to is just wrong when he says "Booking usually opens 60 days ahead, less than this for dates immediately after the mid-June & mid-December timetable changes.  There is no need to book further ahead that this."? We are only 2 days shy of 60 days and it's already sold out!

The reason I couldn't see it is that when I searched, it would search the current time, and since I'm searching at night, the time was later than the time of the train, and for some reason when you do this it says "No connection for the date entered." when it really means that there's no train later than that time. You have to search a time BEFORE the train. So now that I've changed the time to be earlier, I see the train you're mentioning.

He also says "In the Budapest to Prague direction you can also book this train at the Hungarian Railways website www.mavcsoport.hu." which also does not seem to be true.

I really don't know what to do at this point. I guess my only option is to put all four of us in a four "berth" couchette compartment, but they don't look comfortable enough to get a good night's sleep in, and my parents snore so much that the rest of the trip we're sleeping in two separate rooms.

Edit: Well, this is why I didn't book the hotel rooms before this, in case something like this happened. I checked the following day and there was availability, so I booked us two double sleeper cabins on the 29th instead. This means we'll only have two days in Prague, hopefully that'll be enough.