The doomsday argument is normal

I think he is describing the paradox of supernatural predicting power suggested by the doomsday argument and SSA in general. It will boost the probability of scenarios with a smaller reference class. Like in the sleeping beauty problem, SSA suggests the probability of heads is 2/3 after learning now is Monday, even though the toss is yet to happen.

Following similar logic, the astronaut can boost his survival chance by limiting the number of people saved. He can form this intention: select and reheat the passengers one by one. As soon as he feels he has been reheated halt the entire process and let all the remaining astronauts die. This will link his survival to a smaller reference class, which can boost its probability. How much will it help depends on the "correct" reference class. If the correct reference class only entails the astronauts then it would be very significant. If the correct reference class includes all "observers" in the universe then the increase would be marginal almost zero. But nonetheless, it would be greater than 50%. 

This conclusion is very counter-intuitive. E.g. if I have been reheated, should I keep to the intention of killing the remaining astronauts? How can it still affect my chance of survival? It seems retro-causing. 

I consider this a counterargument against SSA and the doomsday argument. But I like this thought experiment. It shows in order to actually conduct a sampling process among a group of agents that includes the first person, it has to forfeit the first-person perspective. e.g. from the viewpoint of an impartial outsider, in this case the security cameras

Interest to DA peaked in 2000s and now is declining

This actually demonstrates the problem further. If using "civilization" as the reference class then as you said humans would stop thinking about DA in about 50 years since it started 50 years ago. But what if we use "people thinking about DA" as the reference class? Due to the internet giving it more exposure, there are a lot more people thinking about DA now than in the 80s and 90s. If I am in the middle of all these people, then we would likely stop thinking about DA a lot sooner.

Similarly, human civilization has existed for about 5000 years so it would exist for another 5000. But for much of history, the global population is way less than a billion. We are likely around the 100 billionths human every born. So if use each person as the reference class then with the population boom the end shall arrive much sooner. 

The forecast of the future changes drastically when different reference classes are used. So for DA to be valid there must be an exclusively "correct" reference class. But they all seem arbitrary. 

I've read your linked post, and it doesn't convince me.  The reasoning doesn't seem rooted in any defensible principles, but is rather just using plausible-sounding heuristics which there is no reason to think will produce consistent results.

The example of the person placed on the unknown-sized grid has a perfectly satisfactory solution using standard Bayesian inference: You have a prior for the number of cells in the row.  After observing that you're in cell n, the likelihood function for there being R rows is zero for R less than n, and 1/R for R greater than or equal to n.  You multiply the likelihood by the prior and normalize to get a posterior distribution for R.  Observing that you're in cell 1 does increase the probability of small values for R, but not necessarily in the exact way you might think from a heuristic about needing to by "typical".

To illustrate the inconsistencies of that heuristic, consider that for as long as humans don't go extinct, we'll probably be using controlled fire, the wheel, and lenses.  But fire was controlled hundreds of thousands of years ago, the wheel was invented thousands of years ago, and lenses were invented hundreds of years ago.  Depending on which invention you focus on, you get completely different predictions of when humans will go extinct, based on wanting us to be "typical" in the time span of the invention.  I think none of these predictions have any validity.

While sun-rise problem setup is somewhat crazy, the bus waiting problem is ubiquitous. For example, I am waiting for some process to terminate in my computer or file starting to download. The rule of thumb is that if it is not terminating in a few minutes, it will not terminate soon, and it is better to turn off the process.

Leslie in "The end of the world" suggested a version of DA which is independent of assumptions of probability distributions of events. He suggested that if we assume deterministic universe without world-branching, then any process has unknown to us but fixed duration T. For example, the time from previous bus arrival to the next bus arrival is Tb. It is not a variable, it has fixed value for today and for this bus, and Omega may know it. Say, it 15 minutes. It doesn't depend on the way how arrivals of other buses are distributes, are they regular, normally distributed etc. It is only for this bus.

Now you arrive on the bus station. You only know two things: the time from last arrival and the fact that you came in a random moment relative to bus arrivals. In that case, you can estimate time until next bus's arrival according to doomsday argument logic: it will be around the same time as from previous arrival. 

But chances of the alignment are small? Like less than 10 per cent? Also, AI can solve DA once and for all.