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Greetings MsvSpaz,
If the app is region locked, your biggest problem is not so much installing the app, but how the servers will respond to you network I.D.
If Google Music is not allowed to work in your region, the servers will most likely not allow you to connect to them.
I don't know of any way around that, sorry.
Once you've uploaded music to Google Music it doesn't care where you are.
I had the app installed on my Nexus but you can sideload it by downloading from a reputable source.
I update it via Xda: [APP] Google Play Music 4.3.609 - xda-developers - should be the latest version AFAIK.
Once you've successfully downloaded the music manager onto your PC using a vpn terminating in the US you should be able to upload over your normal internet connection. I'd suggest testing with a single track first - easier to delete from Google Music via the web interface than a whole collection.