"With all that said" in spoken English, contradict or not?

One can surely say 'The literature has covered < one aspect of a problem > < ... like this, for example ... >. With all that said, I would like to focus on < different aspect of same problem >.' and have no contradiction or implicit 'though'.

With all that said just means you are not going to say that again, and that you are not going to directly address what has been said -- that it is past, and we are moving forward.

I do know know how this is usually described in English but it is a form that in Latin was known as 'the (ablative) absolute past participle' (since in Latin it must be stated in the ablative.) This form is no more special than others.

With all that moved, only my clothing remains in the old place.

does not create feeling of contradiction, only completeness. There is perhaps some light emphasis laid upon refusal to continue discussing stuff other than the clothing.

"With all that said" can be used to indicated a contrary argument, but is often used to notify the speaker has reached the end of additional or tangential information and is ready to return to the main topic.