It helps to look at your dominant 7ths. A dominant 7th can only appear in a single major key - and it will be the fifth of that key.
For example, the first two lines of the progression are the same but they include a G7. A G7 can only occur in the scale of C major. F major, which would be the fourth of the C major scale is the first chord. The second chord is C major. So from the perspective of C major, it is a 4-1-5-5 progression.
The G pedal tone on the first two chords is also a clue, the G being the fifth of C major. G is also a normal chord tone with G7 and C major, but is being extended to the F major.
So what seems to be appropriate for playing over this part of the progression would be G mixolydian mode. This maintains the overall "G" feel of the progression. The notes would be C major starting on G - G, A, B, C, D, E, F, G.
The next two chord lines is essentially the same 4-1-5-5 progression, but now we have changed to the F major key - per the same reasoning for the first two lines - C7 can only occur in the scale of F Major. Since the C pedal tone is the dominant factor here, C mixolydian would be appropriate which would be F major starting on C - C, D, E, F, G, A, Bb C.
You might take note (no pun intended) that the only different note between the common notes is the alternation between B and Bb.
(Gee, I really hope I got that mixolydian mode name right!!

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