Answered: 3 special barrels 1 circular goal - a clarification

The manual says this:

So according to this, if there were three doubler or negation barrels in a goal then only one of the two similar ones would count and it would cancel the opposite one, leaving no net change. I can’t see how this can be read any other way.

However, this thread says this:

Which is correct?

The thread you referenced has been updated to reflect the exact position mentioned in the manual. Your interpretation of <SG8> is correct.