Hello Ian,
Before you spend any money, my bet is on the fact you have the jaws mixed up in the slots. I am assuming the chuck ran true before you took it to pieces
#1 usually has the least amount of scroll engagement on the first 'tooth' into the scroll, #2 progressively more and most with jaw #3. Are the jaw slots numbered and for that matter the jaws themselves?
If the jaws are not numbered and you stand the jaws on a plate on the gripping surfaces, you will see the progressive effects I mention. Number them 1 to 3 accordingly
If the chuck jaws are not numbered either, then assemble the chuck with your newly marked jaw #1 into a slot so that it just clicks into the scroll as you wind it anticlockwise when looking at the face of the chuck. Then wind the scroll clockwise until the start of the scroll just shows in the next slot round [also clockwise] Engage the jaw as I described and do the operation again for the final jaw.
Now test the chuck for run out, note the value and take all the jaws out again and repeat the whole sequence starting this time from the next jaw slot round in a clockwise direction. Test again for run out, note the result and repeat the whole thing again for the final slot. You will then have three set of run out readings.
Pick the best and build the chuck up accordingly, but this time mark positions permanently in some way. It is a lot of work but the only way to get it right in the absence of any helpful jaw and slot markings
Regards
Brian