Murdoch said he tried to respond to the concerns by adding more trees to nearly complete the circle.
Reynolds said the park service consulted Islamic experts who saw no Islamic references in the design.
"I feel badly that [Burnett] has bought into the conspiracy theory," he said, "because none of it is true."
Joanne Hanley, the park's superintendent, said, "The NPS will build the memorial as designed."
But Burnett says unless the design is scrapped, he will withhold the use of his son's name, which historians say would leave an unacceptable hole in the story of Flight 93.
"Future citizens," said Reynolds, "have a right to know the names of those on the plane."
A long road lies ahead before any ribbons are cut here.
In all, 60 acres in the 1,000-acre heart of the park have been acquired, although officials say negotiations with major landholders are progressing, and fund-raising is $17 million shy of the $58 million needed.
Supporters remain firm in their belief that the park will open, even if incomplete, in four years.
After all, they say, these were the citizen heroes of 9/11. Since that heartbreaking day, hundreds of thousands of people have taken a 15-mile detour off the Pennsylvania Turnpike to pay them homage.
Many visitors leave something behind - a baseball cap, a flower, or small message. Because no official place exists to hold their thoughts, they write on whatever is available. The parking-lot guard rails are covered with their words: "We will never forget."
The unarmed passengers and crew - among them a retired special-ed teacher, an arborist, a software salesman and college students - defeated the hijackers' plot to use their plane as a missile to attack Washington.
"This was an act by 40 heroes, one of the most selfless acts in the history of the country, not a grand military campaign," Murdoch said, in describing his effort to build a memorial that is both bold and understated. "These were everyday people who did something extraordinary."
Contact staff writer Amy Worden at 717-783-2584 or aworden@phillynews.com.