If the teeth arn't moving, but the counterbore is, it is actually a distortion. The stress relive ideas are good, this should be done just prior to finishing the dimensions you wish to hold. But;
Nitrided parts can distort due to the internal stress created in the nitrided layer. If the part is uniform in section, and the part is nitrided all over, these stresses are quite balanced and little distortion occurs. Some odd shapes produce unbalanced stresses, hence the movement. (in gas nnitriding, there is also a uniform additional change of about .0007 in. added on each surface due to white layer).
You can try to mask either the inner or outer surface of the counterbore and see the results. You may be able to modify the movement this way. Masking for nitriding works well, and for production processes a masking ring may work. Whether you can control the process to your tolerance requirments is another issue. Hope this helps.