This is because the current position, direction, and speed of an atom (and all other measurements that can be done physically) are only possible with one and only one specific history of everything else in the universe.

This seems almost certainly false. You can measure those things to only finite precision—there is a limit to the number of bits you can get out of such a measurement. Suppose you measure position and velocity to one part in a billion in each of three dimensions. That’s only around 200 bits—hardly enough to distinguish all possible universal histories.

It’s a tempting thought. But I think it’s hard to make the math work that way.

I have a lovely laptop here that I am going to give you. Suppose you assign some utility U to it. Now instead of giving you the laptop, I give you a lottery ticket or the like. With probability P I give you the laptop, and with probability 1 - P you get nothing. (The lottery drawing will happen immediately, so there’s no time-preference aspect here.) What utility do you attach to the lottery ticket? The natural answer is P * U, and if you accept some reasonable assumptions about preferences, you are in fact forced to that answer. (This is the basic intuition behind the von Neumann-Morgenstern Expected Utility Theorem.)

Given that probabilities are real numbers, it’s hard to avoid utilities being real numbers too.