I'm not saying it's not a Simonsen - but it has very unusual features. Simonsen made a variety of cantilevered boxes, hip roof and no hip roof (like yours), with a number and wide variety of trays and configurations, but the big ones had folding lids with a very distinctive asymmetric design, where the clasping lid and the shorter lid met in a very distinctive sharp angle shape. That one doesn't have it. Also, and this is really what caught my eye first - I have never seen any Simonsen with side carry handles! I could be wrong. Again, I'm not saying it's not a Simonsen. But if it is a Simonsen, it would be a very unusual Simonsen that is not very common or well-known. (LOVE the two-man side carry handles!)
EDIT: Here's the lids difference I am talking about...
EDIT: Added another side shot that shows it even better, and on an earlier box, without the later rounded edges, for a better comparison.