OMG, I finally fixed it - well, on my other PC anyway. It was these instructions that finally allowed me to do it.
Uninstall the software and make sure everything related to it is deleted then install this → http://support.logitech.com/en_us/product/g27-racing-wheel/downloads
The current Logitech drivers no longer support the G27 except as a Driving Force, which means all the buttons on the front will act as the same button in addition to other loss of features. As well as downloading no version of the gaming software newer than 5.10.127 as linked above, there are some hoops to jump through to keep the G27 working every time there's a Windows 10 update that loads new Logitech drivers.
After uninstalling all current drivers and software:
Open a Command Prompt, and type "cd %temp%". This will open your Windows temp folder. Note the prompt shows the folder location. Use File Explorer to go there and note what folders are present. Then run the installer for the 5.10.127 software and drivers, and watch for a new temporary folder to appear. Make a copy of that folder somewhere else for the future so you can skip this step next time.
(note by sfinktah: the directory name is random, there will be 3 directories made, just look for the one with the 2b-LGS folder in it).
Navigate to that temporary folder (or the copy you made) and then go further into 2b-LGS-x64/Common64/Logitech/WMDrivers. Right-click on the file wmjoyhid.inf and select Install. Then launch the WMWizard.exe application.
You may need to unplug and replug the G27 after that, but I think usually I don't have to.
(sfinktah: neither did i, in fact, i didn't even uninstall the old drivers)