At least for the Model 29, the feet required extensions. (Or you have to narrow the bottom (above the "inverted T") of the lower half of the rings.
With the 586, maybe the "regular" Millett rings work? I've been trying to buy a friend's for many years, but never thought to compare and contrast the 586 and 29!
A close-up, angled shot of the rings on the 586's barrel will reveal any difference.
I have the info for the Millett rings or at least S&W's P/N on an old thread, but won't search for it until more is revealed about the .357's version.