Relative intervals when playing over chord changes

I have been playing guitar for two years, and I am trying to learn improvisation over chord changes. I'm trying to figure out how people visualize the fretboard. For example, say I'm in C major and the progression goes C > G

Currently I basically change my reference point after every chord. So during C I visualize the C roots and know that I should focus on 1-3-5-7 (and more largely the ionian mode). And during G I visualize the G roots and know that I should focus on 1-3-5-b7 (and more largely the myxolidian mode). The problem is that "changing the reference" after every chord is pretty difficult for me, and I don't know whether I just need more practice or this is the wrong approach.

I recently listened to an interview of Ariel Posen saying that he doesn't think of modes, he targets chord tones but brings them back to the tonal center (e.g. if you want to target the 3rd of the 5 chord, that's the 7th of the I chord). To me thinking "I should target 5–7–2–4" over the G chord seems very difficult, but is that the more common way of doing things?

Thank you