my two cents
My advise is to paint it! Sure it is lettered for an interesting outfit, but you need to focus on the Maple Valley, How does a Westside Lumber Company locomotive happen to be on you premises? Sure locomotives got bought and sold, as well as leased, but they were huge expenditures for these outfits, and they got usually lettered and numbered pretty quick, as a matter of corporate pride.
Then you add the other dimension. The West side lumber company was a 3 foot gauge outfit. While they did have a standard gauge Heisler as a mill switcher, it was a Small narrow gauge Heisler that was put on standard gauge trucks, and was tiny compared to Your unit which s oversize even for a standard gauge unit.
A well done model railroad , which you are well on the way to creating; is like a play, or a Novel. We want to look at these little models, and get some suspension of disbelief, and build a different time and place around them in our mind. Most every thing should fit neatly, and what doesn't should have a plausible story. That story should ideally work for both the uninformed viewer ( the kid down the block), and the visiting expert . According to My Grandfather Vandyke ; an expert is someone who knows more and more about less and less until they know everything about nothing.
Now some anachronisms and anomalies will work, as long as the whole structure of the illusion is strong enough to support it. Say for instance that heisler was a perfectly scaled model of #3 the Westside mill switcher, had a custom paint job, with exquisite lettering and weathering; and you couldn't bear to touch it. (as far as I know, such a thing does not exist commercially in HO). Then it would be worth making up a story to explain it.
Instead, you just have a mass produced model, that is lettered for a lumber company because it is famous , not because it is appropriate for the locomotive in question. If you letter it and number in in a similar fashion to the shay, you can make them look like thy belong together. I even change stacks to get that family look, and paint most of the cab roofs red ( that is easy and cheap). Locomotives are main focal points for your operation, all or most of them need to do their part to help establish corporate identity.
You don't have to re paint the whole locomotive either, you can dry brush black over the lettering, and blank out the letting very effectively. That is what I did with the USRA 0-6-0 I lettered for the J. E. Patterson Coal and Lumber Co. for our club.
Bill Nelson