Sentences beginning with "I do not think (that)" vs. "I think (that) + negation"

Among the following sentences (assuming they are all grammatically correct, and hopefully seem natural to native speakers as well):

1. I do not think the overwhelming majority of the countries in the world would agree with your opinions.

2. I think not the overwhelming majority of the countries in the world would agree with your opinions.

3. I think the overwhelming majority of the countries in the world would not agree (or just say "would disagree") with your opinions.

First of all, I assumed that 2) and 3) are different: let’s say 80% is an overwhelming majority, then my understanding is that 2) claims that only a significantly smaller percentage of the countries agree, e.g., 60%, or 50%, or 40%; while 3) claims that 80% disagree, which means that at most 20% agree.

If my understanding above is correct, then which ones are equivalent? I feel that 1) is about the same as 2), but from the grammar I learned from school, 1) is supposed to be another (more correct/common?) form of 3). Any native speaker to tell?

The answer to a relevant question seems not satisfactory: "I think that … not … " and "I don't think that …"