Let's first take the inverse of the fact stated about Scrooge, removing "not" from the matrix clause and into the that-clause complement:
He was so ... dreadfully cut up by the sad event ... that he was not an excellent man of business on the day of the funeral.
We might expect a person to be a little shaky and off their game when a close colleague dies. But Scrooge was still on his game, contrary to normal expectation. In present day English, we might expect to find the fact of Scrooge being unshaken stated in the following way, with not appearing in both matrix clause and complement:
He was not so ... dreadfully cut up by the sad event ... that he was not an excellent man of business on the day of the funeral.
The car was not so damaged in the collision that it could not be driven to a repair shop. It did not have to be towed.
In the 19th century and earlier, the reversal could be expressed not with a double negative but with but that with the meaning "to the contrary":
He was not so ... dreadfully cut up by the sad event ... but that he was an excellent man of business on the day of the funeral.
The horse was no so lame but that it could be ridden to the blacksmith to be reshod.
... The passage was not very dark...there was a window over the
back-door that threw a light into it, and also a light over the
street-door, so that it was not so dark but that she could perceive
every thing transacted in it.
[source: The Universal Magazine of Knowledge and Pleasure: Containing News, Letters, Debates, Poetry, Musick, Biography, History, Geography ... and Other Arts and Sciences; which May Render it Instructive and Entertaining to Gentry, Merchants, Farmers, and Tradesmen. To which Occasionally Will be Added an Impartial Account of Books in Several Languages and of the State of Learning in Europe; Also of the Stage, New Operas, Plays, and Oratorios. Volume 67. London 1780.]