So the strong form of the phrase "free speech must mean freedom from consequences" implies all speech must mean freedom from all consequences, whereas the weak form would mean all speech must be free from a certain undefined subset of consequences?

That phrase is always proposed as a rebuttal to "freedom of speech doesn't mean freedom from consequences," and always in the context that any consequences given will lead to a slippery slope. It doesn't contradict that premise at all if interpreted in the weak form, it only makes sense as a rebuttal in the strong form.

So either the so-called "free speech maximalist" side actually believes that people who argue free speech doesn't mean freedom from consequences are referring to all consequences rather than any consequences, or else we're all just in violent agreement with one another, and really just haggling over what those consequences should be.