Summary for the impatient
Disclaimer: the solution described does work for my particular circumstances. Can’t guarantee it will work for you. 🙂
Go to your device’s Settings, open Location Services (if you have them enabled; if not – you can stop reading now), scroll right to the bottom past the text describing location icons, select System Services, and disable everything that doesn’t appear to make sense to you. I left only Compass Calibration and Mobile Network Search on. I also turned on Status Bar Icon so that I can see if the phone is accessing location services for longer than feels reasonable.