The essay treats the Veil as the experiment and maximin as what you would pick. Rawls's book is a thicker machine.
A Theory of Justice (1971), §24: the original position is the fair situation in which parties choose principles for the basic structure. The veil is one constraint on that situation. The parties do not know their class, talents, conception of the good, or "the special features of [their] psychology such as [their] aversion to risk." They also "have no information as to which generation they belong."
What they choose is not a welfare decision rule. It is two principles in lexical order (§11, restated later in the book): first, the most extensive equal basic liberties compatible with the same for all; second, fair equality of opportunity, and only then inequalities to the greatest benefit of the least advantaged — the difference principle — consistent with just savings. Liberty is not tradable for a higher floor.
So the axiological load is already in the device: what you are allowed to know, what you are maximizing (an index of primary goods, not welfare), and which principle may not be sacrificed. Calling the output "maximin as a risk preference" drops the first principle and the hidden risk-attitude.
The named competitor for the decision rule, eighteen years before the book, is Harsanyi.
"Cardinal Utility in Welfare Economics and in the Theory of Risk-taking" (Journal of Political Economy 61, 1953) puts an impartial observer behind a lottery over positions and has that observer maximize expected utility. That is average utilitarianism, not maximin. In "Can the Maximin Principle Serve as a Basis for Morality?" (American Political Science Review 69, June 1975, 594–606) he says maximin as the original-position rule "would lead to absurd decisions," and that he had the expected-utility version before Rawls's first paper on the subject.
Section II already lists expected value as a menu item. Harsanyi is not a reprint of that list. He is the claim that once you set up impartiality as a lottery over who you are, expected utility is what rationality requires, and maximin refuses ordinary acts that have a tiny chance of a worse worst case.
They split on a test Rawls himself wrote. §24 hides the parties' risk aversion, so "Rawls assumed extreme caution as a taste" is the wrong leftover. The leftover is whether the original position's information constraints select maximin (§26) or Harsanyi's average. Discriminator: a policy that slightly risks a worse floor and greatly raises almost everyone. Maximin rejects it. Harsanyi takes it if the expectation is up. Physics-plus-time does not pick that row; both rules can be run with a long horizon.