Something to try over the G#dim chord: G#dim is the vii of A Harmonic minor, so you could play A dorian over the Amin7, and switch to one of the modes of A Harmonic minor for the G#dim. Personally, I would use the ii mode, which would be B locrian in this case ( the ii chord of A Harmonic minor is Bmin7b5 ).
Judicious use of the harmonic minor and it's modes will add instant Yngwie to your playing ( and that doesn't have to be a bad thing ). Just try not to play all 64th notes while striking rock-god poses. There is an excellent series of books by Don Mock ( an educator at GIT, and well known session ace and jazzman ) that covers the different minor scales and their applications, the one on harmonic minor is "Harmonic Minor Revealed!" I can't recommend this book enough if you are looking to instantly spice up your playing with some exotic sounds.
Out of the loop? I didn't know there was a loop!