I think Dr. Leiserowitzs’ suggestion is most accurate. In a memo written by my great grandfathers sister (written after the war), she writes that at first they (her parents and siblings) were taken to a forest where they were forced cutting down large trees and preparing wood. In the end of 1941 they were set free [?] and went to the nearby town Byisk.
Once in Byisk her brothers found work in Barnao which makes very much sense to actually be Barnaul as suggested, which is around a days trek from Byisk (160 km).
What troubles me most is obviously the lack of personal records that the Russians might still have. Sadly the Russian still boast about “thank us for saving the Poles from the Nazis”.