I found the below "Traveling Set" picture within the posted book I have had for many years.
Unfortunately, the Author does not go into any fine detail, no Manufacturer or date.
He did not bother to explain the contents of the box.
The box appears to be similar to yours. The lid looks as if it could open up to reveal a mirror? But of course he does not bother to make any additional information, with the exception of "Traveling set in fine wood, silver and ivory with several drawers"
However......It does appear to have a so called "Boot Pull" on the edge of the middle drawer that looks like a button hook on the end. It is separated by a "Corn Knife" perhaps? Than another folding instrument with a different tip, similar to yours you posted in your "Utensils" photo.
Sorry about the picture quality the book is from a small 5X8" paperback with poor paper quality.
I ran a quick search on the Author, but discovered nothing. Mr. Krumholz was 38 in 1988 when he published the below book. That would make him only 67 years old now.
Nice find Mike, very interesting piece.