What kanvasman says about centering the motor teeth with the regulator teeth makes sense.
One because the motor stops turning before the glass is completely up and the other is that the motor attempts to continue to move the window down even after it hits the stops.
The only other reason I can think of is that the regulator teeth have been ground down to the point that there are no teeth left for the motor to engage with.
I’m going to pull the AIM and shop manual for my 73 and see if there are any instructions regarding setting up the motors and regulators that’s different than for the manual windows.

 

I looked through my AIM and Shop Manual.
There is nothing in the Shop Manual.
The AIM doesn’t mention anything about installing the electric motors and only one illustration shown below.
I did notice there is a difference in the adjustment procedures between a coupe and convertible for 73.
I did notice this operating effort guide shown below and don’t know if it’s any help or not.

 

Here's a pic of the PW regulator - the side we're looking at faces out when in the door.

Yes, you could well break a finger or worse if the spring isn't restricted - imagine scissor-action between the long arm and the mount plate. This only applies out of the car, when inside the car the weight of the glass and tracks keeps the spring tamed. (Keep in mind the spring is pushing the glass up to assist the motor.)

The gear section only pivots about 20° and the arms are limited by the tracks they're in: the long horizontal at the base of the glass and another short horizontal above and to the rear of the motor mount area of the door. It's been a year or two since I worked on mine, but I don't believe there is any up/down adjustment of the regulator mount to the door to lift it ~1/2".

I agree that if the teeth are damaged the regulator may not swing through its entire arc - but they'd have to be bent or packed with something because missing teeth would cause the motor to grind or freewheel at the end of the gear.

4-vettes, When the window is all the way up by the motor, can you manually raise it further by pulling upward on the glass?

 

Can I manually lift the glass? No.
Does the motor spin or freewheel at the top indicating missing teeth? No.
I had a long talk with the owner of the car today. He is reluctant to go back in and find the problem. My previous adjustments have his windows 10 times better than they were. And this small gap at the top he'll just live with.
Me, I'd want it right. But I think he's afraid of what we will find and spending money on what he feels is a small problem isn't likely to happen.
I thank you all for all your suggestions.

 

Each end of the sector gear (big gear on the regulator) will stop the PW motor, as intended. It sounds to me that the sector gear is not aligned to the regulator. The holes that line up to place a nut and bolt thru to prevent regulator movement before taking the motor off, more or less align the sector gear and regulator. So, when the window is raised in full up position and is short of being completing closed, check the sector gear position to see if there are any teeth left on the sector gear and stops the motor. I'm not sure if this was clearly explained. What I'm saying is if there are no more teeth to allow the regulator to move the window up, it stops.

So the question becomes why? That would basically mean the regulator is out of sync (sector gear to regulator) not a motor problem. You could have an incorrect regulator or a mis-manufactured regulator, like a hole drilled in the wrong position. That can lead to a fix. If in fact the regulator does not have any more teeth to move the window up, then the sector gear needs to be repositioned. A question I have is when the regulator and sector gear are bolted to lock the regulator, are there an even number of teeth above and below the intersection of the motor gear and sector gear. I don't know how many additional teeth are needed to allow the regulator to raise window to full up position.

I may be getting ahead of myself here, and need to wait to see if the motor gear and the sector gear are at max movement when window stops. This is going to be difficult to see, so concentrate on the sector gear position in full up position. Then lower the window an inch or two, then look for the position of the sector. You may have to guess if the regulator is running out of teeth. I would think that in the stopped position, if you see a good portion of the sector gear away from the motor gear, that would not be a problem. i hope this is not too confusing. I also hope that this can be observed in the door.

 

Did the owner remove the regulators to mount new motors? They are riveted in. Maybe used bolts to re-mount them and regulator gear is hanging up on a bolt preventing glass from going all way up?