There is also this very cool observation, though: the subjective theory of value is also a private theory of value.

Menger identified this insight, and Mises later developed it further: value is subjective. It originates in the evaluating mind, not in the evaluated object. No “objective value” exists independent of someone’s valuation. Prices emerge from the interaction of subjective valuations; they do not measure pre-existing objective values.
For privacy, this has immediate implications. An actor’s valuations exist in their mind. No external observer can access another’s value rankings directly. They can infer preferences from observed choices, but the underlying subjective experience of valuing remains internal and private.

I had not before considered the ideas in that second paragraph. My subjective valuations of a thing are subjective because they are my own and not immediately obvious to anyone else.

I keep coming back to this being a praxeological innovation/claim to improvement... that deliberation is a separate stage of decision-making/action.

I also suspect it's WRONG

As in: there is no separate deliberation. Economically, there's just action. Yes, we can all introspect and see "hm, yes, I thought about this a ton and I went pro and con on whether to buy that car..." but the economic/praxeological value is in the moment of signing/acting/making the purchase -- nothing else.