" Suppose that going to sleep or losing grasp of your surroundings opens a wider space of worlds you could exist in, which jumps you into another reality along with consistent memories of it. "

There's no you to jump in dust theory, There's just a succession of mental states , which appear to form a temporal contiguous being because one state contains memories of "previous" ones. An interruption to the structure would be much ,more analogous to death t than to "you" finding "yourself" in a strange new world.

Look, the first question boils down to: does my unconscious mind affect my measure? If so, than it isn't much different from being awake. If not, then all my problems seem to apply.

In what sense do you think your conscious mind can effect your measure.....and why care? Your measure may be tiny in absolute terms, but it will always seem like 1 to you. If you want to avoid short .or unpleasant futures, your best bet us to follow commonsense advice about life and health preservation. Dust theory can guarantee that "you" .. a mental state containing your memories up until now...would not suddenly start experiencing a weird world, ..... that is the essence of Egans argument against it....but doesn't suggest that remaining conscious would make any difference. You seem to think that consciousness exerts some force that "keeps things together", somehow, but dust theory is nowhere near so causal.

At the scale of QM and quantum physics, there is no unconscious mind as distinct from conscious mind - there are only particles, fields, and forces. That's it. There's precisely nothing about the conscious mind that would inform the physics of the universe/multiverse to do something different from the unconscious. You're chasing shadows.

Further, dust theory strikes me as a possible map of reality, much like timeless QM and copenhagen interpretations are also maps - but ultimately, they aren't the territory. Nobody gets upset because it's possible to count natural numbers out of order; being upset because "oh noes the states of the universe might be out of order" is equally pointless.

I think you're looking at it wrong. However much magical reality fluid there is in you going to sleep in an orderly universe, there's the same amount in you waking up in one.

I think we can refine this problem by imagining that someone sets up a machine to 1) fully scan your brain and surroundings, 2) kick off a simulation of you, 3) spend a real second running it for a subjective second, 4) end the simulation and idle for a real second, 5) goto 1.

You could respond with terror at the 50% probability of death you face every two seconds. Or you could think it was pretty neat that half your subjective moments get double reality fluid. Personally, I think if you're going to count a decrease in MRF as a loss you should count an increase as a gain.

So if sleep is a large temporary gain in MRF, savor that. You're communing with a vaster, stranger experience-set, and all the MRF you send in will come out. You can't change how much MRF you send to the 'yourself waking up' experience, but you do have some ability to redirect it between 'yourself waking up groggy' and 'yourself waking up well-rested'.

Of course, you exist in every possible world which would produce that mindstate, but some are 'vaster' than others, leading you down the most probable courses.

This is basically the answer. You can think of different worlds as having different amounts of "magical reality fluid," or "measure." You are more likely to be in one of the worlds with lots of magical reality fluid - if there are two worlds with a 2 to 1 ratio of magical reality fluid, and you otherwise have no information distinguishing them, your probabilities about which world you're in should likewise have a ratio of 2 to 1.

Suppose that going to sleep or losing grasp of your surroundings opens a wider space of worlds you could exist in, which jumps you into another reality along with consistent memories of it.

There are no jumps. There is nothing to do any jumping - no soul, no thread of consciousness above and beyond your physical state (at least not when it comes to assigning probabilities - when it comes to utilities, you are allowed to value continuity of experience or content of your memories if you want). In any given world, you either exist or you don't. If you go to sleep in this world, the only way to leave is to die in your sleep.

The idea of sleeping being simpler than waking, and therefore there being more sleeping boltzmann brains of you than waking ones, is interesting, and debatable, but basically irrelevant. You go to sleep, you wake up. The boltzmann brains evaporate back into their constituent atoms. Life goes on.

Speaking of empiricism: you have fallen asleep many times, and nothing bad has happened..why should something bad happen next time?

I was thinking about the same problem and my conclusion was and is the following.

1. Lets assume a demon model, which move simplified part of me in trillion different copies. Is it a problem for me? No. It is logical to conclude that it will do it trillions times, so I will eventually return into my original myself, and will not notice any difference.

2. It will be some kind of natural selection in dust world lines, which will result in more stable ones, and most likely I am already in such line. In this line dreaming is built such that it will not result in important shifts of reality. And it is true: dreaming is not unconsciousness state. I start to have dreams immediately than I fall asleep. So dreaming is built to be not interupting some level of consciousness.

3. Someone may try to use the flux nature of reality for magic. You must close your use, forget everything about your self, imagine that you have 1 000 000 dollars, forget that you imagine it, and just keep this feeling. Than you open your eyes it would be more likely that you have 1 million dollars. While it seems to be ridicules procedure, it strikingly similar to traditional human magic, which always include trance state and visualisation of desired things. If natural selection exists in dust world lines it would help beings able to rise its reproduction chances by magic, so nothing surprising here.

4. You do not need Dust theory for all it. You could get flux reality from some interpretation of QM. Just imagine that you live inside large Schrodinger cat.

I've never heard of 'Dust Theory' before, but I should think it follows trivially from most large multiverse theories, does it not?