Try the Redding "Pro" crimp die.
It has a sort of compound taper-roll that has tested as the best one against bullet creep (albeit in the 44 magnum).
The 44-40 is the only "44" I don't load or shoot as it is not a .429-.430.
I do know the brass can be fairly thin at the mouth.
The Lee might not be the perfect crimp die for that brass.
I only use a Lee crimp (the collet crimp) in 444 when crimping against the nose of a WFN.
The 44 taper crimp die I use is from RCBS.
Redding make one as well I think.
Check those 2 for a 44-40 taper crimp die if you are not going to try the "Pro" crimp.
Actually any normal roll crimp die should work fine in the 44-40 once you get the touch if you are crimping into a cannelure.
I understand it's somewhat easy to crumple the brass with too much force.

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NEMO
"Everything 44"