Help! U.s Stamp #544 Green George Washington One Cent Stamp(S) Encased In A Peculiar Box

I recently acquired a round wooden box with a painting on the top of it, slats in the sides but no way to open it. I had the box for about a week trying to find out what the painting on the top of it was and never even noticed the stamps inside. One day my memory finally came back and I realized that the painting on the front of the box is actually a painting of The White House with the damage from the war of 1812. I went and grab the box and looked inside the best way I could and that's when I noticed the two stamps inside which are green, #544 US George Washington stamps. The stamps have been pushed through the slats on the sides of the box and the adhesive is still visible along with a little dust. I do know that these types of boxes were originally made by native Americans, but that is all I've been able to find out. The painting on the front does match the damage to the White House from the war of 1812, and I have found a couple of stock photos that were taken at the time but differ just a small bit. It almost seems like someone was sitting somewhere close by when they painted the picture on the front because the painting is in color and we all know we only recently obtained the ability to add color to older photos. There is a name written on the bottom of the box and I have done some research which led me to a census from one of the first colonies in Georgia and that census come from about the time frame when George Washington was in office. I need more information because it's driving me nuts!

I don't think a "couple of stock photos" were taken in 1812.

Fun story. I expect once you thoroughly investigate the 1c green Washington stamp, that the cute box will be worth much more than the stamp inside. The stamp is Scott #804 printed in 1938 (a penny stamp, literally), or a coil stamp depending upon its perforations (still a penny stamp). I like the box, which is the item that should be investigated.

Somehow my first thought was:
Looks like an artist rendition of the Simplon Hospice around 1900..

The backdrop's right, but what happened to the middle?

The backdrop's right, but what happened to the middle?

It's not how the stuff is organised in reality. No fool would build a large house smack in the middle of the glacier's path. The artist likely wanted to paint both the hospice and the glacier "neatly arranged".
In reality, the hospice is to the left of the image (at least I think. Long time I traveled there. It is a really spectacular train ride from Chur to Tirano with the Bernina Raetian railway. All assuming the image does show the assumed region).

Good piece for Antiques Roadshow. Not so much for us 'cause those stamps are not 544s.