I've never actually heard of mountain men using a camp box, but I'm sure they would have had access to boxes the traders no longer had use for after rendezvous. I have pictures of dozens of supply boxes from Forts Washita, Osage, and Gibson. All of these are not painted, but plain pine boxes. That doesn't mean that they weren't painted by trappers though. Seal skin trunks were also used during this time period. Pitch and rosin is mentioned on a few trade lists, along with "black varnish". But, this doesn't support the fact that they painted boxes with it. And, at the same time it doesn't mean they didn't either. We just don't know.
Indians out West used red, verdigris (green) and yellow ochre, along with various berries and bark to color moccasins, clothing, parfleche, etc. The mountain men very well could have picked up the use of parfleche, especially if he had an Indian wife.
If you have a lot of camp gear like I do, use a box, parfleche and hemp or canvas for your stuff. These are all documented, and would also show the variety of things the mountain men used to transport their goods.
Just a thought.
Pare-