Things I look at and "smith" with a new lock. The very first thing I look at is the tumbler axle- full-cock notch/sear nose-pivot screw geometry to be sure its at 90 degrees. If its not, I send the lock back, although I have corrected some. Polish all contact surfaces as you did. With the mainspring and hammer removed, look for lateral play of the tumbler between the bridle and lockplate. If there is more than .005" play I carefully file the surface of the bridle that abuts the lockplate to get <.004" movement. Careful here, the surfaces have to remain flat and parallel. I look at the tumbler axle fit in its hole in the plate. I don't want any discernible slop here. If there is, I bore out the hole in the lockplate, press in a bronze/iron bearing and drill /ream it to fit the axle. I look at the small tumbler axle and its fit in the hole in the bridle. Again, I don't want discernible slop. If there is, I will turn the axle down to about 1/8" diameter (or to the size of an appropriate number drill) and polish it, drill out the bridle hole to a suitable size, press in a solid piece of bearing bronze and using the hole in the lockplate as a guide drill/ream it to the size of the axle. I look at the fit of the frizzen in its slot between the plate and pan-arm and shim to remove play. I pay particular attention to the sear nose and the full-cock notch, bringing those mating surfaces to mirror bright--don't change the angles!! I usually work on the sear spring to reduce its force--they are ALL too heavy.
Is all this necessary for a functioning lock? NO. Like Mike said, put it together and see if it sparks. But all the above will serve to improve lock-speed by reducing binding and friction and, for me, its worth doing.
