It would also be worth emailing the museum to see if you can get their sources for the skin.
The men behind this airplane are like a 'Who's who in the Aviation World". I am sure the folks at HTC not only know this plane but all of the following names:
"Fokker/Redfern Dr. 1 Triplane Replica History - N105RF
EAA’s Fokker Dr. I was built by Walter “Wimpy” W. Redfern (EAA 143). Walt was born in Joplin, MT in 1921. In his teens, his excitement for flying was fostered by watching movies of WWI featuring open cockpit biplane fighters. While growing up, he spent his time building model airplanes and learning many skills from his father. Most of these skills would be needed in his future homebuilding endeavors. In 1938, Walt completed flying lessons and received a pilots license. He served his country in WWII and married his high school sweetheart, Velda Warwick. After the war he put his impressive skills to use on the construction of a Payne Knight Twister (1949). He completed the aircraft and flew it for many years, but the idea of owning a WWI fighter was always in the back of his mind. In 1958 Walt sold the Knight Twister and began looking for a project.
Walt found his project while looking through a flying magazine. There was an ad for “Triplane” plans from Peter Bowers of “Fly Baby” fame. He ordered the plans and began researching the design in earnest. For additional insights into the Dr. I design he acquired some Joseph Nieto plans from the Smithsonian, but his greatest find was yet to come.
During his research he was able to get in contact with Reinhold Platz, one of the original designers of the Dr. I. Mr. Platz sent Walt a wealth of information along with a set of original plans. Even with the language barrier, Reinhold became a valuable mentor to Walt.With Walt’s’ impressive skills in almost all facets of airplane building, he was able to create an authentic replica of the Fokker Dr.I. Modifications were made as follows: the engine is a 1938 145 hp Warner Scarab seven-cylinder radial engine, it has a larger fuel tank to hold 30 gallons, and larger oil tank with a capacity of 5 gallons. The back of Walt’s garage in Tekoa, Washington was a busy place for three and a half years. It took 4000 hours and $4000 dollars to build the replica triplane.
Once completed, the triplane was escorted through the small town of 900 by volunteer fire department trucks and local police. What a site it must have been! The first flight was made on July 24, 1964. Walt flew the airplane for approximately two years and 500 hours before selling it to Mr. Robert Fergus.
Walt Redfern went on to build 12 additional aircraft and founded Redfern & Son’s Custom Aircraft, Inc. He constructed four additional Dr.Is, two Great Lakes, a French Nieuport 14, a Starduster Too, de Havilland DH2, Sopwith Camel, Bucher Jungmeister, Albatros DVa, and a Fokker DVI. Walt passed away on February 25, 1996 before the test flight of his Fokker DVI. Thanks to Walt Redfern’s skills, passion, and hard work, many aviation enthusiasts can enjoy the sight of WW I fighters in the skies above, and the possibility of building one themselves."

Edit: Bold Print in case it was missed. This bird was built with the guidance of one of the
original Dr1 designers. I am quite certain Herr Platz knew exactly what Weiss's several a/c looked like.