I agree with @MarvMills that "indoctrination" has a similar meaning but is a step down in negative connotations.
When you want to make it positive, you say "education". I don't mean that all education is brainwashing, but rather that social and political activists often use the word "education" as a euphemism. They'll say, "The public must be educated about this issue", meaning, "people must be browbeaten into agreeing with us". (Well, one could argue that all education is a form of brainwashing, but that's a different question.)
I suppose "brainwashing" is an extreme form of persuasion. At least, in the sense that you are discussing the use of the word here. If you take it that way, you could list a whole range of words for persuasion with varying degrees of "intensity", like brainwashing - indoctrination - education - pressure (as in social or political pressure) - persuasion - dialog. No doubt many other words.
BTW, bear in mind that what one person calls "brainwashing" another would call "teaching common sense" or "presenting the facts". I've had many conversations about controversial issues where someone who disagrees with me at some point says, "You've just been brainwashed by X!", where X is some group that agrees with me. Of course I'd say, No, it's not that X brainwashed me, but that I found their presentation of facts and logic more convincing than that of group Y.
Like in your example, you say you're thinking of groups like Mormons and Jehovah's Witnesses. I'm not a member of either group and, let's say I sincerely doubt that what either group says is true. But by what standard would you say that what the Mormons do is "brainwashing" while what Catholics or atheists or CBS News or Harvard University or the Libertarian Party or whoever you agree with is "attempting to persuade people" or "presenting a rational case for ..."? Maybe I'm not disagreeing with you, maybe that's your point when you say that "brainwashing" can be a "considerable exaggeration".