"We've got about, I'm guessing 1400 or 1500, well past the goal of 1000," Preesman said.
The final boxful of cranes still had to be threaded and added to the display, which the pair would have finished in time for World Peace Day.
The display is expected to stay in place for a couple of months.
The paper crane became a symbol of peace following the story of Japanese girl Sadako Sasaki who lived in Hiroshima during the atomic bombing.
After being diagnosed with leukaemia from the radiation she began folding origami cranes, motivated by the Japanese legend that granted a wish if you made 1000 cranes.
The United Nations General Assembly has declared International Day of Peace as a day devoted to strengthening the ideals of peace, both within and among all nations and peoples.