I'm just going to post a quick response -- I think you may be thinking about this too technically! Music theory is not "static" and you can switch from any key, to any chord, to any melody or note whenever and wherever you want. Of course, it might not sound "pretty", so to speak, but that doesn't mean you are not "allowed" to do it. You are thinking too much in classical music theory rules. Classical music theory is the starting point, the foundation of modern harmony, but now it is up to you to be the experimenter. You need to try this out and use your ears! Try out any reasonable progression you can think of to connect these 2 sections. This could be through testing out all chord combinations in both keys, moving to a different key in between, etc (infinite possibilities).
In fact, I know I have experimented with this progression before, and recall it working, but its all about the preceding bars getting you there and the bars getting you out. And that is something that might take you quite a long time to develop, feel out, and hear in your head. Try improvising as many melodies and lines as you can to mix these 2 parallel scales. I don't think it should be too hard, since they are both of the root A. Vamping on a single root note usually sounds great with Phrygian Dominant, and you may be able to do a simple sudden modulation between the two scales. And, you may try out a ton of stuff and just never find something that sounds like it works, to you, and abandon the song all together! This is all a part of becoming a better, and more creative, developing musician.
One of the most satisfying and awesome things for me as I have developed musically, is to be able to connect some seriously weird scales, chords progressions, and just generally out there music together, improvising on the fly. And it's definitely not something I can do every day! When inspiration strikes, it can strike in some amazing ways that you have never heard or imagined before. (Hopefully you get it recorded, though! If so, lucky day)
Edit: And look, no real theory mentioned in this post.