If I'd known you had a post 1962 Single Six (before that all Rugers had XR3 grip frames), I'd have suggested it from the start.
I swapped my first grip frames about 52 years ago when I only had a 44 flat top (XR3)and a 1964 first year Super Single Six (XR3-RED), and that was the only two Rugers I owned.
The good news is the alloy grip frames are not fitted to the guns so the fits are all pretty much the same, good to mediocre. Therefore, the easiest swap there is; no fitting required.
All my single six size Rugers have XR3 grip frames, alloy or steel. Except a few with shortened barrels that have the 32 Mag Vaquerito short Xr3-RED steel frames.
Super Single Six old model with XR3 steel grip frame:
Single Six old model with 32 Mag Vaquerito short Xr3-RED steel frame: