Assuming we're still in A minor, let's try a different set of strings.
This time, rooted on the A string, let's try out each set of chords, layering first with simple 5ths, an added octave, thirds, and so on.
Just because the first note of the chord is not the root note, it doesn't mean that playing through chords in this format doesn't work. It's simply a different vantage point.
Again, visualize the A minor scale from the starting point of the chord. Understanding scale intervals based on different starting points will engrain a firm knowledge of scale-play on the fertboard.