White glue was used later in the war. I know for sure dou, dot, and byf used white glue stocks quite a bit from 1943 and on. Bcd also used white glue in late 1944 and 1945. Also it seems like here and there you can find pre-1943 white glue stocks from ar, byf, and others but maybe those were just from reworked rifles.
I'm sure mr. farb or Bob in Ohio has a much more clear idea of the white glue stocks. I also would like to know more!