These test conditions and choke impedance are creating a very high Q factor of about 390. The specification of the ATi is very wide at this point, and for good reason, because a very small error in the measured phase angle of the impedance will create a large difference in reading. This will be an issue on all LCR meters as well. The ATi and AT3600 look more unstable than LCR meters under these conditions because they make measurements much more quickly using a fraction of the averaging used by a typical LCR meter.
I would recommend lowering the test frequency of the RLS test (to lower the Q value) or using a DC R measurement for very accurate resistance results. At the expense of slightly longer testing times then the integration level set in the editor program can be increased from the default of 'medium' to 'long' to give a more stable result. If the average value of the result is still not acceptable then a 'user offset' value can be set in the editor program to effectively calibrate the result to a desired value. If none of these techniques are acceptable then please let me know some more details of your application and I'll see if there's an acceptable way to perform the test using the ATi. We normally find however that the ATi stability is more than acceptable for production testing of parts.