A bit of an update.
The new unfinished grips arrived and 3 coats of Tru-oil and 5 hours later they both looked great and improved the controllability of the pistol.
I also traded off a truly horrible S&W Bodyguard for store credit and said "why not" and used it to get another Star BM. I got the pick of the litter with this one and it cleaned up really well and since it was detail stripped for cleaning when the grip arrived it got the grips. I've ordered a second set of grips for the other Star BM as well.
This 'new' Star BM was made in 1977 with a serial number in the 1,435,9xx range. You'll note the purple area where the frame was spot annealed and then drilled to prevent any cracking. My other Star BM, made in 1979 with a serial number in the 1,508,5xx range seems to have had this done at the factory. Consequently it appears Star made a change somewhere between these two pistols.