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.