The data should only be exchanged between the browser of the user and Google Drive.
I don't want to have to maintain a Google hosted application. Is this possible?
The only point of apis console is to register your applicaiton or in your case script with google. Its baslcy just there way of keeping track of whos accessing what i think. Once you have it registered you normaly would use a clientid and stuff as well as Oauth2 to allow users to access there google drive with your script. But you wont need to go into that becouse its your application thats storing its data there and not a user.
You will probably want to look into a service account. https://google-developers.appspot.com/drive/service-accounts