I think we get too wrapped up in authenticity. The rifles built by the Hawken Brothers and later J.P. Gemmer were not mass produced. We have all read that they could be built to order for whatever the buyer wanted. Just take a look at the originals pictured in Baird's book. All sorts of variants.
The Thompson Center guns were based on sporting rifles of the era. I have a Seneca in .45 caliber. It is a modern made rifle along the lines of a New England sporting rifle.
The Hawken rifle was built for hard use in a rugged environment. It was heavy and like a earlier post mentioned meant to be carried on horseback or wagon, not still-hunting.
There were certain features that were somewhat consistent. Buy the best one that you can reasonably afford and have fun with it. Jake, Sam, or J.P. are not around to tell us what is authentic. We have to settle for images, surviving examples, written documentation, and creative license.