A file management app that supports Google Drive and can access the Documents folder is rare; generally third-party apps aren't allowed to access the Documents or Downloads directories, which are where Word (and other first-party Office apps) store their files. One such file is Pocket File Manager (also called PFM; I have no connection with this app other than having used it for years). I stress that it might work, but also might not. It supports many cloud providers, including Google Drive, and is also very unusual among third-party apps in that Microsoft allowed it to access the Documents directory. If you use PFM to access your Google Drive and open the file with it, there's a chance it will work. (It's also just a useful app to have.)
Unfortunately, you'll probably either need to continue re-sharing files back to Google Drive and dealing with the outdated duplicates, or get a new phone. It's a pity there's no proper successor to the 1020!
Some background on the problem you're having:
WP apps - including the MS Office apps - cannot read from or write into the storage of other apps (such as Google Drive). When you open a file from Google Drive, what is actually happening is that the OS is making a temporary copy of the file in a location that Word (or whatever; I'll use Word in these examples as it's used for most kinds of text file) can access, and then opening Word to that temp file. Word knows it can't save the file back where it came from, and the only places it can save to are things like your Documents folder... which Google Drive doesn't interact with (although I think OneDrive does, even on 8.1).
You might be able to get around this with an SD card; WP8.1 makes it easy for devs to add SD access to their apps, so Google Drive can probably access it and Office definitely can. However, if I recall correctly, the 1020 doesn't have an SD card slot (which is absurd, given the size files its camera creates, but c'est la vie). WP8.1 doesn't have "virtual SD cards" (where it's actually just a directory on the root storage) the way Android does, unfortunately, so without an SD card slot there's no location where third-party apps (like Google Drive) and first-party apps (like Word) can both access the same files.