E mixolydian (or major) to E Phrygian dominant to A harmonic minor
E phrygian dominant and A harmonic minor are - as you know - the same scale, so you are not exactly going from one "to" the other. It's the chord change that will make that same set of notes sound different.
The choice on the E is yours of course - but personally I would choose the same scale for all the chords.
(That's simply a matter of personal preference. In a sequence changing as quickly as this, I like to keep the same overall tonality if I can. You may prefer the disruptive effect of scale switching - and so might I sometimes!)
E mixolydian(or major) to E Phrygian dominant to A phrygian
E mixolydian(or major) to E Phrygian dominant to E Locrian
A phrygian and E locrian are the same thing in this case. "E locrian" over an Am chord will come out as A phrygian anyway. No point thinking of it as anything different.
I'd agree this is a good scale for the last Am before the change, to anticipate the approaching tonality (C mixolydian). (At least a good idea to try it, see how it sounds.)
One way of helping you decide is to come up with a melody - something you can sing over the whole sequence. Certain notes (and therefore certain) scales are going to feel more "right" than others when it comes to melody construction. A melody will give a coherence and a logic to the whole thing.