I have a Verizon GS4 as well and for some background, in my Maps settings I have:
Location Reporting set to update automatically
Report from this device unchecked
Enable location sharing unchecked
Enable location history checked
Automatic check-ins unchecked
I have it that way to enable the Google Now cards I want (I have all of them enabled) but not automatically share my location in stuff like Facebook and Instagram.
I was seeing the type of Maps usage you're seeing until I went into my Application Manager and uninstalled updates for Maps. It seems as if it's reinstalled them as I haven't seen any negative effect, but my Maps usage is down at like 5% now. My "Google Services" is higher but my overall battery life is better. Of course, YMMV, but it's easy to try.
I also have location based profiles in Tasker, so it's checking my location based on net but not GPS.
I also have the Qualcomm Battery Guru running, but I don't think that's had a big effect. It seems like it mostly just stops certain apps from needlessly refreshing, but it doesn't give a lot of information about what it does so that's just a guess. I have the WiFi part of it turned off and WiFi active all the time.