The letter, signed by Edward Coryell, who heads Local 8 of the Metropolitan Regional Council of Carpenters, repeated the argument that his union did sign the agreement by May 10, when its contract extensions expired.
Coryell's letter said that the signed agreement was hand-delivered May 9 but that convention center chief executive John McNichol declined to accept it.
Since then, two show managers who have produced conventions at the center, said efficiencies have improved with the work being handled by four unions instead of six.
The letter suggests that, because all six unions have signed, all should be allowed to work.
Without naming names, Coryell's letter attributes the carpenters' woes to "ulterior motives and personal agendas at play."
Three union leaders, including John Dougherty, president of the powerful International Brotherhood of Electrical Workers Local 98, led their workers past a May 12 protest set up by the Teamsters after that union was barred from the building.
Coryell's letter also referenced an article published in Sunday's Inquirer describing how companies who produce conventions at the center mark up labor costs, a standard industry practice nationwide.
"Unwilling to tackle this problem, [Gregory Fox, the Convention Center Board's chairman] was content with the status quo," the letter said, "and continued to perpetuate the myth that the unionized workforce was the cause for high exhibition costs."