Josephine Do you think it's a good idea to turn the drop screw a little bit to see if this fixes the problem of AlvinC's piano?
No. That's just adjusting things willy-nilly. To do the job right, everything needs to be adjusted correctly. But the staring point is having a somewhat correct repetition spring tension. And as an overly strong repetition spring is one of the main reasons for the hammer not checking on a soft blow, the best place is to start there.
I'm assuming the back-check itself is set close to correct as in the video the two hammers checked in a near identical place on a firmer blow.