Having looked at a variety of kits for this project, the closest that I found was the old Pyro(?) bomb ketch - if I recall - came out to ~ 1/150th - consistent with Lindberg's La Flore and Heller's 74s.
Commercial wood kits like Sultana could be used but would have to be built to an "off" scale since the Lady's keel is about the same length as Sultana's hull.
There is a commercial built up wooden Lady Washington for about $200 and who knows how much shipping and insurance.
The best approach may be to carve your own hull and go with commercial fittings. The Gray's Harbor Historical Seaport printed an 18 X 24 sheet with Ray Wallace's preliminary layout (including lines) and a 16 X 20 waterline hull and rigging sheet. There was also a six part series on the construction of the Lady by Richard Miles in "Seaways" magazine throughout 1990, with lines plans, photos of construction and some detail drawings. Check with Gray's Harbor...
Ray Wallace designed the Disneyland Columbia and was hired in the 80s to do a seaworthy version - but economics dictated a build of the smaller Lady Washington, instead. The Lady's hull was supposedly patterned as a 2/3 scale replica of a late 18th century, deep draft "clump" similar to Vancouver's supply brig, Chatham. This accomodated the installation of diesels, prop shaft, watertight compartments, etc required to meet Coast Guard requirements. When the original Lady rounded Cape Horn in the late 1780s, she was rigged as a sloop - a very impractical rig for inexperienced, volunteer crews - so Ray designed her replica in the Lady's brig configuration that she carried in the late 1790s.
A more historically correct design was reconstructed by Hewitt Jackson (NOT the tax guy) and the plans are on file at the Oregon Historical Society. For her role as a trading consort for the Columbia, the orginial Lady would have been a sloop with a very shallow draft - much different than today's Lady. The plans for a similar sloop, that Hewitt also reconstructed, can be found in the book, Log of the Union, John Boit's Remarkable Voyage to the Northwest Coast and Around the World, 1794 - 1796, by Edmund Hayes - available through addall dot com's used book page for less than 10 bucks. This book is well worth the money if you have an interest in the Lady and the northwest coast maritime fur trade.
The story of the Columbia and Lady Washington can be found in Columbia's River, by J. Richard Nokes, also available for less than a trip to Starbucks on addall.
As an aside, the Lady's film credits will be soon expanded - I was involved in the shooting of several scenes aboard her under sail, flying the old Spanish ensign (for which my patient wife had to sacrifice a queen size bedsheet) for a documentary on the colonization of California and the founding of the California Missions. The Lady is nearly identical in length and close in rig to the snow San Antonio, which carried Father Junipero Serra to Monterey in 1770. The five part series will air the third week of November to commemorate his 300th birthday. This is the first time Spanish Alta California's maritime history is getting air time.