The SuS so closely matches, for instance, the SuS in their catalogs and also, I think, the grips on their handguns that even without the caveman marking I'd put the Steigleder Drilling down to Sauer. As you say, Steigleder's Suhl shop was apparently just for sourcing and several accounts suggest this was primarily or exclusively from Sauer & Sohn.

There is now a gun museum at Zella-Mehlis that would perhaps be able to help identify some of these stamps and their owners and/or would better know the relationships between various families. The Sauer family tree, starting with Georg Adam Sauer, gunsmith born Suhl in 1673, is published in the new book JP Sauer & Son by Peter Arfmann and Rolf Kallmeyer.