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LingakuLingaku综上所述 + ，+ [clause]
综上所述 starts the last paragraph or sentence of a piece of writing and introduces the conclusion drawn from everything before it. It stands at the very start, followed by a comma. It is written – essays, reports, papers and exam compositions.
Literally it is "pulling together what was said above", so the clause after it should follow from points already made. A new argument doesn't belong there.
总之 "in short" also closes an argument, works in speech, and can cut a discussion short as well as sum it up. 综上所述 only follows a worked-out argument in writing. 总而言之 sits between the two. 总之 has its own point.
The phrase is fixed: 所述 can't become 所说, and 所以 in front repeats the "therefore" it already carries.