How to approach Iminor - VIImajor progression in a functional harmony way

I am wondering how one would approach a Iminor – VII major progression.
In a simple form something like: Am Am G# G# (just triads)

The idea rose from practicing melodic minor (in a jazz way, so same down as up).
Although the VII chord of melodic minor is half diminished, the VII th mode in melodic minor is (again, in jazz) often used on dominant chords, hence my idea using a major instead of a b5 triad on the VII.
My idea was to play A-minor over the I chord and A-melodic minor over the VII chord, thinking of this chord as a non resolving dominant, playing the altered scale (superlocrian) over it. Essentially i thought i would be able to play straight A-melodic minor over the whole progression, but this sounds ‘not as it is supposed to be’.

The feel over the G# is very Lydian. Lydian dominant sounds good over the VII major, and lydian sounds even better (because the fourth, Db, clashes somewhat with the Am, changing it to a D (making a #4) was my idea).

The feel of this progession is also very chromatic mediant to me, which led me to think as Am as a substitute for Cmaj, making the progression a chromatic mediant. However, the feel gets totally different (obviously) when starting on a major, instead of a minor chord. So, i abandoned this idea.

My question:
How would you approach this progression, thinking in a functional harmony way. I know how to approach it thinking of them as two seperate chords, but how are they connected?

I know you can play anything you want, but since i am no theorist ,but find it very interesting, i was wondering how one would approach this progression thinking of it as a whole instead of two seperate chords.