Still not sure what you are asking, and your prickly tone is kind of strange.
I like A ionian to G lydian. Love that sound.
Are you asking for compositional help with where to go next? Someone suggested F# aeolian. The I, VII, vi progression is one I love - check out Sister Cheyrl by Wynton Marsalis (its in B). And you might get ideas on where to take the tune after that.
Are you asking on how to analyze your idea theoretically? You can do it several different ways. It's partly gonna depend on where the tune goes after this. You could certainly write it with three sharps and nobody would bat an eye.