Since JKR wrote the story, she can use preknowledge to make HG arbitrarily smart, and since she doesn't have too large of an impact on what actually happens

That's arguable but if true it would also demonstrate the point. An actually rational agent in her situation would have made a significant impact.

she can do this without needing to account for how smart HG is; even if she were to devise some genius plan to beat voldy, she'd have to act through HP, who could easily and stupidly reject her plan offscreen.

No. That would not be a HG:MoR story. That would be Hermione Granger and the Excessively Upgraded Idiocy All Around Her.

That is, I'm arguing that even if you kept making HG arbitrarily smart (but not arbitrarily powerful or prophecy-choosen), you could easily keep everything else the same by making HP or some other characters arbitrarily stupid, possibly offscreen.

This just isn't true. I think you drastically underestimate the difference between the smart and conciencious girl as conceived by Rowling and an actual rational upgrade of Hermione and the consequences that would have. An arbitrary rational Hermione, even with the only the IQ of canon!Hermione, would be an active agent. If not, it isn't Methods of Rationality at all. It's Methods of being a Responsible and Slightly Clever Schoolgirl.