I reload 32-20 and, while the stories seem to be correct about the thin mouth walls of many/most/all factory ammo (I have been able to inspect only 4 flavors of same, btw) I have found the new Starline brass that I buy to be much more robust.
That said,
FROGO207's advice about carefully centering the dies is very good advice.
Also, easy on the crimp ... inattention to this during setup on a couple of occasions has resulted in winkled, unusable cartridges. I keep those 2 accordioned cartridges on the shelf in front of me as a constant reminder.
Some folks avoid that issue entirely by using a Lee FCD (Factory Crimp Die).
I do not know about 44-40, but 32-20 doesn't recoil very much so, usually, not much crimp is required. I
OOPSed those cartridges when I was adding a heavier crimp to see if it worked to improve Trail Boss performance.
Didn't work, btw ... oh well ...