You are begging the question. Whether we believe only truths if determinism is true is exactly what is in question. You have to show that Huemer's inference to this conclusion is invalid or that one of the premises is false, not simply stipulate that the conclusion is false.

The original premise 3 doesn't include an explanation of why S does A. Your reformulation of 3 doesn't just explicate the meaning of determinism, it changes the premise entirely. Huemer doesn't provide a definition of determinism in the text. But whatever determinism is, by his stipulation, if it's true, then at any given time you only ever have one thing that you can do (if S can do A, S does A).

You can define determinism through physical laws and prior states of the universe if you like, but that doesn't really impact the argument. How does the ability of beliefs to influence past states of the universe come into this at all? Huemer reasons that the premises entail that if determinism is true, then free will is true. This isn't meaningless, it's just taken to be a contradiction. Through reductio ad absurdum, he concludes that determism must therefore be false.

Why would you think Huemer interprets P1 in that way when he explicitly has the ought implies can principle as P2? Obviously, if you can't believe the truth about something (because you don't have access to information, for example), you can't be obliged to believe it. In the comments, Huemer is explicit that P1 is meant in the sense of "if P is false, then you should refrain from believing it."

That's an intermediate conclusion that Huemer makes, not a premise. You can't just dismiss an argument on the basis that you don't believe in the conclusion. I'm not sure Huemer's argument is sound, but it definitely doesn't depend on whether people who consider themselves determinists believe in the truth of the conclusion. The implausibility of the conclusion is exactly what makes the argument useful and philosophically interesting, because it is supposed to make the determinist position untenable!

You're interpreting "we can only believe the truth" as "it is impossible for us to believe anything but the truth", while the relevant sense is clearly "it is possible for us to hold true beliefs without any false beliefs." Huemer does infer the former is true if determinism is true in step 5, but he needs the third premise for that (If determinism is true, then if S can do A, S does A.)

Also, the conclusion isn't necessarily self-defeating, it just seems implausible.