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.