There is one way for you (personally) to evaluate the 'worth' or 'differences' between latest/greatest Moodle vs Google Classroom (where one could inspect the backend and new filesystem without investing any $'s for hosting - nor running into any roadblocks in hosting else where). Install a locally hosted Moodle 3.2. Get that running first. Then make a no user backup of one of your 1.9.13 courses. Restore to the localhost Moodle 3.2.
Hint: you don't have to use Moodle's bullt-in Google Respository. Since you are already in a Google Edu domain one could make urls (simple web links that have sharing controls set to members of your Google Domain) to those docs/files where the controls for access are at Google. Any changes to the Doc/files, show everywhere there's a URL link to them. No download/upload/clicking alias, etc..
In the long run ... think it's a matter of 'ease of use' when it comes to Google Classroom/Domains. Have observed that teachers that desire/like more 'control' and/or 'sophistication' in a class/course(s) continue to use Moodle although they are loosing technical support from local IT staff. The latter will eventually mean the end/demise of Moodle in a 'typical' K12 entity, BTW, as most teachers in K12 really don't have the desire to learn how to admin a Moodle server ... the apache/php and especially the DB admin part (locally hosted or remotely hosted).
Interfacing Google with Moodle, if you desire 'ease of use' would also mean setting up users on Moodle differently ... where Google is used for authentications OR students/teachers would have to login twice .. maybe three times ... @workstation @Moodle @Google. The time to work on that is at beginning of the school year ... not at semester.
I'll PM you a link to a Moodle 3.1 tinker site where you can use your Google credentials to create an account. Once you have done that, drop a line and I'll create a category for you to 'play with' - even attempt to restore a *no user* backup of one of your current courses, IF you like.
'spirit of sharing', Ken