To hear the frustration some go through with the factory tachs.
I’ve not had any issues with either one of mine.
For many years I had a used one from a 72 Blazer, and never had an issue with it, even when I put a Mallory Electronic Conversion kit in the Distributor, to replace the points, until one day the Diode in it “Gave up the Ghost”.
I replaced it with a new factory model, and it works great.
Gauging it against my Digital Multi-Meter Tach it’s within 20 RPM, so I’m not messing with something that works.
I must be fortunate, because I don’t have any of the mentioned isssue.
Good luck on figuring out the problem.
And about your adjust me t question.
Yes the screw on the back IS the adjustment screw for “Fine Tuning” the Tach.
It helps to have someone helping you, because you have to be laying on your floorboard while you adjust the screw. Good Luck