Under increasing pressure from City Hall, the Los Angeles Harbor Department has drafted a plan to move the port's largest exporter of coal and petroleum coke away from recreational areas of the harbor. The preliminary plan calls for moving a port-owned facility used by the export company from the harbor's largely recreational West Channel to a remote area of Terminal Island. The exporter, Kaiser International Corp., leases and operates the so-called bulk loader, a 26-acre facility used to store and load commodities for export. The plan, expected to be approved by the Board of Harbor Commissioners next month, probably will mean that the loader will have to move by February, 1994, officials said. San Pedro residents and pleasure boaters have complained that the facility is the source of black dust that pollutes the air and damages some boats.