Are u using ATWT for sharpening or noise reduction or both? I use MMT myself, which eliminates some of the ringing problems from the get-go. Always use either in two passes...you can do sharpening and NR at the same time, but it is recommended they be separate processes.
For deringing with ATWT, I never use the brightening support. It would be rare to have bright rings after a wavelet transform. I use the dark deringing at half the default value and it works well for me....don't remember what that is off the top of my head, but if it is .1, reduce to .05.
I also use a modified luminance mask to further protect brighter stars. Use HT to protect these areas, i sometimes use CloneStamp to get rid of protection on smaller stars, nebula, etc.
Joe