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Given two previous indications of the name, there is no year needed for "August 20, 1926".
"the storm system" - remove either the second or third word
"A tropical depression first formed on August 20 in the central Caribbean Sea from a broad area of low pressure based on weather reports from weather stations and ships in the vicinity." I'd add a comma before "based"
Is there any further info on what happened before it became a TD?
"Nonetheless, the tropical storm began to move more towards the west" - this is the first indication of movement, so this, compared to the track map, is confusing given the apparent northwest motion.
"Once in the Gulf of Mexico, the tropical storm continued to intensify, reaching huricane strength early the next day north of the Yucatán Peninsula.' - when you start a new paragraph, you should mention the new date. Also, see if you can spot the typo.
When you mention SSHS categories, you should either "reaching Category 2 intensity", or "the equivalent of a Category 2 hurricane", since the SSHS was not around until much later.
When did the ship report that eye and pressure?
"The major hurricane" - this is the first indication of MH, and there is no explanation what it is.
"The major hurricane intensified up until making landfall near Houma, Louisiana at 2300 UTC late on August 25 at peak intensity" - some redundancy there, with "intensified up until making landfall.... at peak intensity." Try rewording a bit
What is the basis for landfall intensity? What about when it dissipated?
No need to link "storm warnings" after previously linking TC watches and warnings.
"eight to 15" - have consistency with writing
"Offshore, a storm surge of 15 ft (4.6 m) was reported" - how can a storm surge occur offshore?!
"were estimated at 120 mph (195 km/h)" - sustained or gust? If latter, that isn't a C3
"New Orleans reported numerous window damage" - grammar?
"An offshore ferry was also wrecked by the hurricane" - where?
Any impact outside of Louisiana? The rainfall map indicates there were other effects.