In the end we decided to go with the vintage fur. But with a twist.
I still wasn't happy with the fur I had on hand, so I dyed it with Nice n' Easy. I remembered hearing somewhere that the Museum of Nature used Nice 'n Easy hair dye to restore the caribou in their dioramas after their fur had faded from decades under the exhibit lights. So I thought I might as well give it a try.
Full instructions on how I made the jackalope are over on Instructables.