Can you let us know if the gyro remains perfect, or if it slowly loses it's calibration? Thanks!
----------
This is a link to an older article re: mobile gyroscopes. Maybe it will help out a few. After reading it, it does seem more hardware-ish : /
http://www.ifixit.com/Teardown/iPhone+4+Gyroscope+Teardown/3156/1
24 hours later, 2 restarts, update to 7.0.2, and a 12 mile rugged mountain bike ride using GPS and the replacement phone still goes to -1degrees. (Which I assume is as good as you'll get with a 5s at this point.)