An extendable wall mirror would help quite a bit. Good luck to you.
My back aches after a shave too - unfortunately the mirror in my bathroom is mounted to cater for short to medium people. I'm 6'4, so some musculature origami takes place for me to see what's going on. Already asked the managers of the student halls about buying my own shaving mirror and mounting it, they said no. The hotel I stayed at in Turkey a few months ago had a great set up and made me realise how much easier it is to shave with an actual shaving mirror than just one mounted on the wall, let alone one mounted at an angle best suited to viewing my jewels.
Do you have shared hallway style restrooms, or is it in your dorm room with a roomate (suite style). If the latter, I'd just hang it anyways with a couple screws. It doesn't do anymore damage than hanging a picture, which is typically allowed.