Don,
I'm not saying that the image of the "colorized" destroyer is USS STERETT, I'm just trying to point out that the "artistic style" of the Ms 12R(mod) pattern is similar to that applied to several BENHAM class destroyers. It is unknown when this photo was taken. The destroyer does have radar (and likely 20-mm guns) installed when this photo was taken. When the BENHAM class destroyers were operating out of Iceland in early 1942, most units had yet to receive radars. When USS WASP and USS WASHINGTON operated with the RN Home Fleet in April-May 1942, most of the USN destroyers had at least a SC radar. The timeframe of Ms 12R(mod) use by the USN saw a lot of experimentation and revised patterns. USS TRIPP holds the record in my files of having the most camo schemes/patterns during WWII career. Unfortunately, there is a lack of photography for many USN ships during late 1941 into 1942 to document what their configurations were and what camo they wore.
The IWM has a few rare images of the destroyers of the DesDiv that USS LANG, STACK, STERETT, and WILSON were assigned to. Here are images of USS STACK and USS STERETT in the late January to 1 February 1942 timeframe at Iceland;
Note that USS STACK's camo matches her March 1942 yard period at NorNY when she received SC-1 radar and 20-mm guns. I had thought this yard period was when she was painted in this pattern, but it appears she had it before arriving at NorNY for her availability.
If this colorized image was taken in the Atlantic, then other BENHAM class units could come into play. I have no image of USS RHIND (DD-404) during this period. But, the IWM does have (I couldn't locate this image while searching their website), but it can be seen at Navsource (note that the date of the photo is wrong, more likely dates in about February-March 1942, based on 50-cal MG's) ...
http://www.navsource.org/archives/05/pix1/0540402.jpg ...