You are correct that the torque formula isn't correct.
The angular momentum does not play into the torque calculation (though it will be part of the angular acceleration). Torque is (modeled as) proportional to current, not speed.
Torque = stallTorque * (current - freeCurrent)/(stallCurrent-freeCurrent)
At stall, current is proportional to inputVoltage (V=IR):
if (speed==0) current = inputVoltage * stallCurrent / nominalVoltage
By spinning, the motor generates a backVoltage proportional to speed:
backVoltage = speed * freeBackVoltage / freeSpeed
Free back voltage is calculated from the residual voltage at free speed and V=IR (R being calculated from stall):
freeBackVoltage = nominalVoltage * (1- freeCurrent / stallCurrent)
and finally, current at speed is again calculated from V=IR, using the residual voltage (applied - back):
current = (inputVoltage - backVoltage) * stallCurrent / nominalVoltage
I leave rolling all this back up into your calculation to you.