I would venture a guess that, whatever the typeface, the S is a chop job. If you look at the lettering within the bottom of the black circle, it appears to be the same style as the initials, but there the S is stylistically what one would expect to see with the other letters. The large S may be a reworked dollar sign, or a grafted inverted question mark.

I agree with Nick and would add that the font in question started out as Century Schoolbook.

the font in question started out as Century Schoolbook

Quite possibly: another source may well be Craw Clarendon Condensed. The bottom of the S might well come from the numeral 3 in that face.