Claiming Ludwig in the Bayesian camp is really strange and wrong. His mathematician brother Richard, from whom he takes his philosophy of probability, is literally the arch-frequentist of the 20th century.

And Ludwig and Richard themselves were arch enemies. Well only sort of, but they certainly didn't agree on everything, and the idea that Ludwig simply took his philosophy of probability from his brother couldn't be further from the truth. Ludwig devoted an entire chapter in his Magnum Opus to uncertainty and probability theory, and I've seen it mentioned many times that this chapter could be seen as his response to his brother's philosophy of probability.

I see what you're saying in your post, but the confusion stems from the fact that Ludwig did in fact believe that frequency probability, logical positivism, etc., were useful epistemologies in the natural sciences, and led to plenty of advancements etc., but that they were strictly incorrect when extended to "the sciences of human action" (economics and others). "Class probability" is what he called the instances where frequency worked, and "case probability" where it didn't.

The most concise quote I could find to make my position seem much more plausible:

Only preoccupation with the mathematical treatment could result in the prejudice that probability always means frequency.

And here's a dump of all the quotes I could find on the topic, reading all of which will make it utterly clear that Ludwig understood the subjectivist nature of probability (emphasis mine, and don't worry about reading much more than just the emphasized portions unless you want to).

First:

Where there is regularity, statistics could not show anything else than that A is followed in all cases by P and in no case by something different from P. If statistics show that A is in x% of all cases followed by P and in (100 − x)% of all cases by Q, we must assume that a more perfect knowledge will have to split up A into two factors B and C of which the former is regularly followed by P and the latter by Q.

Second:

Quantum mechanics deals with the fact that we do not know how an atom will behave in an individual instance. But we know what patterns of behavior can possibly occur and the proportion in which these patterns really occur. While the perfect form of a causal law is: A "produces" B, there is also a less perfect form: A "produces" C in n% of all cases, D in m% of all cases, and so on. Perhaps it will at a later day be possible to dissolve this A of the less perfect form into a number of disparate elements to each of which a definite "effect" will be assigned according to the perfect form. But whether this will happen or not is of no relevance for the problem of determinism. The imperfect law too is a causal law, although it discloses shortcomings in our knowledge. And because it is a display of a peculiar type both of knowledge and of ignorance, it opens a field for the employment of the calculus of probability. We know, with regard to a definite problem, all about the behavior of the whole class of events, we know that class A will produce definite effects in a known proportion; but all we know about the individual A's is that they are members of the A class. The mathematical formulation of this mixture of knowledge and ignorance is: We know the probability of the various effects that can possibly be "produced" by an individual A.

Third:

What the neo-indeterminist school of physics fails to see is that the proposition: A produces B in n% of the cases and C in the rest of the cases is, epistemologically, not different from the proposition: A always produces B. The former proposition differs from the latter only in combining in its notion of A two elements, X and Y, which the perfect form of a causal law would have to distinguish. But no question of contingency is raised. Quantum mechanics does not say: The individual atoms behave like customers choosing dishes in a restaurant or voters casting their ballots. It says: The atoms invariably follow a definite pattern. This is also manifested in the fact that what it predicates about atoms contains no reference either to a definite period of time or to a definite location within the universe. One could not deal with the behavior of atoms in general, that is, without reference to time and space, if the individual atom were not inevitably and fully ruled by natural law. We are free to use the term "individual" atom, but we must never ascribe to an "individual" atom individuality in the sense in which this term is applied to men and to historical events.

Fourth:

Calling an event contingent is not to deny that it is the necessary outcome of the preceding state of affairs. It means that we mortal men do not know whether or not it will happen.

Fifth:

For this defective knowledge the calculus of probability provides a presentation in symbols of the mathematical terminology. It neither expands nor deepens nor complements our knowledge. It translates it into mathematical language. Its calculations repeat in algebraic formulas what we knew beforehand. They do not lead to results that would tell us anything about the actual singular events. And, of course, they do not add anything to our knowledge concerning the behavior of the whole class, as this knowledge was already perfect--or was considered perfect--at the very outset of our consideration of the matter.

Sixth:

A statement is probable if our knowledge concerning its content is deficient. We do not know everything which would be required for a definite decision between true and not true. But, on the other hand, we do know something about it; we are in a position to say more than simply non liquet or ignoramus.

Etc. Probability is in the mind. It is subjective, and dependent upon the current state of knowledge of the observer in question. He seems very clear on this matter.

Back to you:

When he says "class probability" he is specifically talking about this. ...

They do not lead to results that would tell us anything about the actual singular events.

Which is the the precise opposite of the position of the subjectivist.

Is it? Let's analyze the full quote:

For this defective knowledge the calculus of probability provides a presentation in symbols of the mathematical terminology. It neither expands nor deepens nor complements our knowledge. It translates it into mathematical language. Its calculations repeat in algebraic formulas what we knew beforehand. They do not lead to results that would tell us anything about the actual singular events. And, of course, they do not add anything to our knowledge concerning the behavior of the whole class, as this knowledge was already perfect--or was considered perfect--at the very outset of our consideration of the matter.

All he's saying is that taking one's knowledge of the behavior of a class of events the behavior of the individuals of which one knows nothing, and putting it into mathematical notation, does not magically reveal anything about those individual components.

For example (taken from that Mises Wiki link), if you know approximately how many houses will catch fire per year in a neighborhood, but you don't know which ones they will be, transforming this knowledge into mathematical probability theory is no more than a potentially more concise way of describing one's current state of knowledge. It of course cannot add anything to what you already knew.

In fact, this isn't even relevant to the topic at hand. Believe it or not, some people thought probability theory was magical and could help them win at games of chance. This was him responding to that mysticism. I certainly don't see how it makes him not a subjectivist on probability theory, especially when the whole analysis is about states of knowledge etc.