Wad:
It depends on how much of a stickler you or your boss are to being period correct. These lean-tos are very common at all but the strictest events, but I'm not aware of any documentation of the Whelan or Baker styles until the early part of the 20th century. I've heard WWI. A flat sheet is correct, but the unique cuts of the Baker, Whelan, and other styles preclude them from being acceptable if you're interested in being 100 percent period correct. (Or as close to 100% as a person is liable to get anymore.) I haven't read it, but I've heard a good article can be found in the Rocky Mountain Fur Trade Journal (Vol. 2, 2008), from the Museum of the Mountain Man, in Pinedale, WY. Hope this helps.
Caleb