Richard Schler, the then owner of the August Schler company, did not make his own barrels. He relied on barrels made mostly by Wilhelm Kelber. Wilhelm Kelber's "WK" stamp often misleads Americans to assign bolt actions Schler made for the trade to Krieghoff. H-J. Fritze in his book quotes a list of the Suhl guntrade, compiled by the US Army on April 13, 1945, after they had occupied Suhl. It lists four barrelmaking "factories" active then: W.Richard Jger (not related to Franz Jger) at Gustloffstr.34, Louis Kelber at Trbenbachstr.1, Wilhelm Kelber at Beyersgrund 1 and Max Stoll at Dllstr.4/6. Certainly at least these 4 were active before WW2 too.
BTW, the Suhl barrelmakers did not forge their barrel blanks, they only bored, reamed rifled and "knitted" the barrels, that is, they brazed barrels and lumps. Filing, Laying and soft soldering the ribs were responsibilities of other specialised craftsmen. The Suhl guntrade relied on only two forges for their rough parts: the Sauer forge and the Schilling forge, tm S in hexagon, now a technical museum run by very old Mr.Schilling. There was another forge, the Gesenkschmiede in Zella-Mehlis.