I'm not aware of any Class III doubled dies for 1944 cents (true overdates ended in 1901 for U.S. coins). The coin is certainly broadstruck, but maybe you also have a centered double-strike. I can't tell from here.
I believe the number 3 you outlined is simply a simulacrum -- a chance resemblance to a digit by an otherwise random imperfection. Humans are prone to seeing patterns, even where such patterns do not really exist. The 3 is far too small relative to the nearby normal 4 to be a Class III doubled die, a counterclash error, or any other source of normally-oriented raised design elements.
