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I think Essex did not act alone. There are too many indications of other shooters:

http://theadvocate.com/home/4828836-125/rampage-revisited
.... police continued to fire at the building for hours after Essex’s death, fearing there were more shooters....

http://ajas29.tripod.com/massbio.html
For 19 hours after his death police still believed his was not alone.

https://en.wikipedia.org/wiki/Talk:Mark_Essex
Some witnesses claim to have seen another gunman who did not fit Essex’s description running through the hotel. Police in the stairwell next to the cubicle Essex was hiding in claim to have heard two different voices on the roof and two different calibers of rifles being fired despite Essex being found with only one. Some reports claim that after Essex was shot and killed police still received gunshots from the roof and returned fire to a shadowy figure on the ledge.

http://www.nola.com/crime/index.ssf/2013/01/40_years_on_marine_pilot_is_st.html
Shots rang out from various spots in the 17-story hotel, making police think there was more than one gunman. ...
Though officials concluded that Essex was a lone killer, even today many of those who worked to stop him believe that he had at least one accomplice.

The New Zealand Herald
January 9, 1973
Six hundred policemen and a helicopter gunship were used to attack three snipers - one of whom was killed - when they went on a rampage of arson and murder in New Orleans yesterday.

The New York Times
January 10, 1973
Police Superintendent Clarence B. Giarrusso said there was “some evidence of a conspiracy” involved in Sunday’s sniping. But he said he could not say flatly that Essex was part of a national conspiracy to kill policemen, as has been asserted by other officials in Louisiana.

The New York Times
January 12, 1973
NEW ORLEANS, Jan. 11 - The New Orleans Police Department has evidence that there were at least two snipers and possibly three in the downtown Howard Johnson Motor Lodge last Sunday and Monday, and that the six people killed and 15 wounded by gunfire at the motel were shot from two different weapons - a .44-caliber semiautomatic rifle and a bolt action rifle. One of the snipers was said by a police officer tonight to have been a woman.
Police Superintendent Clarence B. Giarrusso said the he is not as convinced now as he was Monday that there were two or more snipers, but that he still felt strongly that there were.

http://www.murderpedia.org/male.E/e/essex-mark.htm
Throughout the night, police reported sightings of other snipers and gunflashes in the hotel.
Though (detective Gus)Krinke thinks the reported sightings of other snipers were erroneous, he doesn’t buy the one-sniper theory.
“I believe there was more than one, and that one of them got out in the chaos of removing the guests from the building,” Krinke said. “He slipped in with that and made his way out.”