I have about 15 Starrett catalogs, and looked through most of them. The catalogs back to 1924 show levels and transits that go in the longer, more narrow boxes. The 1924 catalog shows the box, which does not look like yours.
The 1895 catalog shows the No. 99 transit with a tube that looks like it comes off easily after loosening a set screw. Perhaps it was taken off and stored vertically in the box. Is there any indication that the inside of your box previously had tube or plumb bob holders (nail or screw holes?)?
I have a big gap in my catalogs between 1895 and 1924 if anyone else on here has any of those.
I searched Ebay and did not find any other boxes like yours.
John
WVTools