Have you taken the chuck off and thoroughly cleaned the spindle nose, including any adapter plate the chuck might have by taking it off. Make sure there are no chips or anything in there and make sure when everything is re-assembled things go together nice and straight.
Then when you true the chuck do not true the body; put your precision ground bar in the jaws and true up to that. You should be able to get it true both near the chuck and also a few inches away.
It is only after doing this that you can safely conclude that the jaws are not accurate and if this is what you do determine then you can consider grinding them.
However, putting a spacer at the back of the jaws is not really suitable. You need to load the jaws in the same manner they are loaded in use which means gripping something mnear the front. This can be tricky if not impossible but if these are two piece reversible jaws you can make a ring that is gripped by some small bits of round bar in the counterbore for the jaw bolts to load the jaws near the front.
An open mind is a virtue...so long as all the common sense has not leaked out.