Hi Keith.

My experience is that there is more movement at the extreme ends of the steering box worm gear, to the point the steering arm actually clunks. I believe this is normal and when you think of it, this will only be experienced when making a very slow speed U-turns.

I have made my adjustments when there is excessive "free play" (20-30 degrees)in the steering wheel, by loosening the large nut, then turning the slotted adjusting screw and tightening the locking nut. My rough adjustment is between 5-10 degrees of freeplay at the steering wheel center position. Too tight and you will have no "free play" and feel the steering wheel binding (and likely damaging the worm gear).

Like Steve has said, I have used this method for over 35 years and never harmed anything. If you do not have an obvious leak, then I think you 444 steering box is still sound. Just to confirm your "bench test" I do have a spare steering box and will try to repeat your procedure later today.
--
Cam a.k.a. CVOLVO.COM

Don't know if this will help or not, but here are the adjustment instructions for the later model PV444 steering box, p/n 250051 (this is the one I have on my 57):

Assembly, (part no. 250051)
3...check that the steering shaft turns easily without looseness. When the bearings are correctly adjusted, a torque not exceeding 1 kgcm (1 lb in) should be needed to turn the steering shaft.
7. Fit the steering wheel and attach a spring balance to the outer ring. Screw down the adjusted screw until a force of 0,4 -0,7 kg (14 oz. - 1.5 lb) is required to turn the steering wheel past the central position.

The only thing I recall about adjustment - providing all the gears, bearings and bushings are in good condition - is that the wheels should be in the 'straight-ahead' direction, with the steering gears in the box centered. As long as both front wheels are pointing directly ahead, you're OK.

I understand that turning the steering shaft causes the gears to 'load up' as they deviate from straight ahead. So, get your wheels pointing ahead and loosen the adjusting locknut. Turn the inner slotted shaft to take up any play. There is a rather complicated section on this in my 544 books which calls for a spring tension measuring tool to set the amount of pressure required to turn the gears. Test your work by turning the steering from side to side. If the steering binds up, you've got it too tight and can damage the gears.

I've done this on hundreds of various cars, and it always worked out.

Just in case you can't get the slop out, plan ahead to locate new bushings or gears, whichever you end up needing. I don't have any 444 references here, but I'm sure you won't have any trouble digging out the parts numbers.