Learn English – How to say we provide a synopsis here for details refer to other work in formal academic writing

Both "that said" and "that being said" are common (possibly too common) and perfectly grammatical, and sufficiently formal as well. "Having said that" is also correct, but to be correct the subject in what follows must be whoever said that (usually "I"). For instance, you can say:

• Roses are usually red. That [being] said, they are also…

But you'd have to say:

• I like turtles. Having said that, I will now proceed to show…

That said, if you don't follow it up with "I", many people wouldn't notice anything amiss these days.

"That's been said" is a full sentence (edit: complete clause), and it only means "That has been said". Full stop. It cannot be used to introduce the rest of the sentence in the same manner.

As @ChrisSunami says, if a person judging or grading your paper says "this is the standard", then I'd follow that standard. You could find some authority that disagrees and argue about it, but what would you gain? Even if you forced the person to concede, he might then be annoyed with you and be looking for ways to mark you down. There's no point starting an argument that you really can't win. Just follow the rules you're given.

There are two easy ways to avoid using "I" in a paper:

One, use passive voice. "Suggestions for performing cognitive workthroughs were received ..."

Two, personify the paper. "This paper presents several algorithms for ..." rather than "I present several algorithms for ..."

Oh, a third option occurs to me. I've read technical papers where the author refers to himself by some sort of description in the third person. Like, "The researcher performed several experiments using flux capacitors ..." This is especially true when there are several authors, or one person describing the work of several people. "The researchers investigated ...", "The team considered ...", etc.