Paul, I have used Oxalic acid to remove oil & muck from wood particularly on gun stocks sometimes with a little heat added, works well but it may well raise the grain. No matter if you are doing a full refinish.
The logo, have you considered making a new transfer of the logo, there are plenty of images of Starrett logo’s on the web. Was the tool made in the US or Scotland ?
One problem you may have is many of the boxes were made to pale wood of varying types and finished with a coloured varnish which is almost impossible to replicate and even more difficult to “patch in”
A photo may help but I think my choice would be a complete re-finish and a new logo.
John
PS Oxalic acid is a white powder you mix with water