Hi Sairfingers,
I am using the standard 1,2,3 fingerings for the C major. I am an older beginner (56) and my fingers aren't as nimble as they used to be to make chord changes quickly, especially to that C major, and yes, I am doing finger stretching / fretboard exercises. Other than this issue I am making good progress and I even cracked the dreaded F barre chord, so this issue is indeed frustrating.
I will try the fingering you suggested, cheers