In an infinite universe, the likelihood of existing in some "macroscopic state of the world" like "your brain is inside your body on the earth in the solar system" or "your exact brain is floating inside a cloud of disordered gas the mass of the solar system" is proportional to how many "microscopic states of the world" correspond that that macroscopic state, where a microscopic state means writing down the states of all the subatomic particles and what they're doing. (This is the assumption that the universe reaches thermal equilibrium).

And because the solar system is so orderly (it's not at maximum entropy), there are many, many, many, MANY more possible microscopic states corresponding to a macroscopic state like "your brain is floating inside a cloud of disordered gas" than there are to the actual states corresponding to a real solar system.

I don't understand much of this. My argument is that Boltzmann brains would almost certainly experience chaos. So I would have to be in the 0.000000000000000000001% of Boltzmann brains to observe a rational universe (not to mention one that actually predicts the existence of Boltzmann brains). Yes, the rational Boltzmann Brains actually would outnumber their regular counterparts, but that's talking past the problem. The odds are astronomically higher that something is wrong with your science. Maybe FAI figures out how to create negentropy, or breaks out into another universe, or finds a way to have infinite computing power. You suggested some options yourself. All of these have a probability considerably higher than 0.000000000000000000001%.