Firstly, is this a seven-tooth or two-tooth steering unit? I can't tell from your description. Both designs were available in 1929, the two-tooth design being introduced about May or June, depending upon the assembly plant. It DOES make a difference which unit you have because more adjustments are possible with a two-tooth design. Advice will be different for each unit.
Until you supply an answer, try this: disconnect the drag link from the pitman arm. While someone holds the pitman arm firmly, turn the steering wheel back and forth at the top of its travel. If the pitman arm moves at the same time and in unison when the steering wheel is rocked back and forth, the problem is not in the steering box. Wiggle the pitman arm in the middle of its travel from lock to lock. A little free play is acceptable (but not ideal). If the pitman arm can be moved back and forth noticeably, something's wrong inside the unit or if it's a two-tooth design, the three in-car adjustments need to be made.
However, if the steering wheel can be moved back and forth, yet the helper can hold the pitman arm still, the problem lies inside the steering box. Perhaps the new worm gear is slipping on the shaft or a part was forgotten. Go back inside the box and find out where the slop is originating. If you hadn't put in new parts and this were a seven-tooth unit, I would suspect broken sector teeth. A friend traded for a '29 Tudor that had almost half a revolution free play at the steering wheel. SCARY to drive! Upon disassembly, I discovered a couple broken sector teeth were causing the slop.
Anyway, assuming your pitman arm moves at the same time as the steering wheel is turned, the slop in your steering lies between the pitman arm and the rest of the components. Check whether the remaining three steering arm balls are round or are oblong/egg-shaped (the one on your new shortened pitman arm should be nice and round). Ensure before doing this that the drag link and tie rod end plugs are adjusted properly so that with some effort, you can rotate the shafts with one hand. If either shaft is too easy to rotate or cannot be rotated by one hand, the end plugs need adjusting.
Check these things out first before going deeper.
Marshall