I happen to think there is another notion here - intent. The intent of the "fire!" yeller is somewhat irrelevant since the actual danger is, or should be, minimal.

The is a core part of the disagreement. The cost of preventing risk of injury from a false yell of fire is prohibitive for the owner of the theater. So it is reasonable to shift some of the cost of prevention to the person who knows there is no fire but wants to yell fire, in part because the cost of not falsely yelling fire is so low. Further, it is reasonable to expect the potential false-yeller to know that the yell will be believed, cause panic and therefore cause injury.

The Koran burner receives more protection because there wasn't a knowing falsehood in that case. The relevant mental state is not intent to harm, but knowledge of the statement's falsity.

I find it's easier to think clearly about this stuff if, when calculating the costs on both sides, I try to forget that I have a preferred answer.

The cost of someone shouting "fire!" in a theatre is what it is; I'm inclined to agree with you that it's not very high, though I think you're trying to make it sound lower than it is. The cost of preventing someone from shouting "fire!" in a theatre is what it is as well. Looking at just the first-order costs I conclude that the costs of preventing it are in general lower than the costs of it happening.

The second-order costs are less clear to me and can easily swamp the first-order costs, though. Mostly it becomes a question of whether there's a reliable Schelling point near shouting "fire!" that I expect to prevent that from becoming grounds for supporting higher-cost speech suppression. I'm less certain about that; and I expect it depends a lot on the specific community, so I can easily see where the "shouting fire" legal principle leads to a lot of expensive bad law, and that on balance we'd therefore do better discarding the principle.

Or perhaps not.
If I were actually interested in activism on this issue, I would start by refining my estimates.

As for intent, I'd say it's at least theoretically relevant. For example, I consider the cost of having prevented all-and-only people who wish to shout "fire!" in a theatre for malicious reasons from doing so to be significantly lower than the costs of having prevented everyone from doing so regardless of their intent. That said, the costs of implementing such a policy given current technology are onerous, so I probably oppose (given current technology) having such a law, although various cheap approximations of it might be OK.