It sounds like your worm and sector could be extremely worn if the adjustment scew is that far in. It may also be possible that the body of the sector gear is bottomed against the inside of the gear housing, just above the bore for the sector bushings, not allowing it to be adjusted down towards the worm any farther. Again, the worm and/or sector would really have to be worn out for that to happen.
The steering gear will turn farther than what is limited by the spindle stops on the kingpin lock bolts without binding when everything in the box is in good condition and adjusted properly. When the limit of the steering box is reached in either direction there should be a positive STOP when it gets there. In your case, If you disconnected the drag link at the pitman arm and turn the box in either direction beyond what is allowed by the spindle stops, I would expect there to be a bind towards the end indicating that the worm is worn in the middle but not at the very ends where it's never been used before. Might be worth a try to see if you can tell if the gears are worn out.
Luckilly new worm and sectors are available for '37 and later and are of good quality and, in my experience, set up well during adjustment. These boxes are increadibly simple to work on too compared to the '36 and older. It's no doubt one of the many reasons people with '35 and '36 "upgrade" to them all the time.