I would suggest getting AMK's catalog. It does have a cross reference, pictures of the fasteners, and pictures of the various finishes (i.e. S2)
BTW, 378156-S2 is a 5/16-18x15/16 1/2AF .88 external with an S2 (phosphate & oil) finish.
I would suggest that you carefully note what the head markings and washer tooth type for each location that you remove bolts from. While the Osborn manuals are a good resource to use, they are not always exactly correct for every manufacturing plant or build date.