[RGK20m3]

Well, I think you are on to something.  The dial that I removed was broken along the edge in 2 places, and the center was broken out (it had a 300 degree circular gap around the hub; the remaining 60 degrees was where it attached- I assumed to allow it to align with the guides). This dial has part number 27-5340
The replacement came in an envelope (which I retained) and was marked DS-A571 (or DS-H571); when I go to their website, it says that part is for a 38-116
Before I installed the replacement dial, I compared the graphics and they are the same. But now that you mentioned it, I checked and both old and new scales are compressed at the upper end (a little over an inch from 1500 to 1600, but an inch from 530 to 580).
Even though both the 38-116 and the 38-690 have magnetic tuning, are the dials calibrated differently? I did have to file a notch for the hub to locate on the replacement dial.....they both use the same tuning condenser on code 125.