I am by no means an english language expert. But i can't think of an instance where a double negative would create extra emphasis, without sacrificing understanding or perception.
'I am not unconvinced by his argument' vs. 'I am convinced by his argument'.
The argument was mildly persuasive, but not forcefully so.
Talk as you may, for i will not stop you, but never will you find me using phrases such as 'I haven't not', 'We didn't see nothing', 'She never danced with nobody'.
Although we can make sense of such phrases, within the structure of such usages tends to create an intrinsically biased perception from the listener in most circles. That you either are 'uneducated' or that you aren't credible with what you are talking about, whether either are true are beyond the point.
I don't disagree with you on the bias, unfair as it is, and I don't expect you to use language in a way you find uncomfortable.