Assuming that by "GAPPS" you mean the Google Play Store etc., my strategy has been as follows:

- copy all data to a computer

- wipe the phone

- set up a google account with bogus information

- install all the apps i might ever want to use

- delete the account info and remove google stuff

- copy personal data back onto the phone

This is a big hassle, so I only do it once a year or so, but it seems to work ok.

Of course I have no way of verifying that the phone actually deletes my data when I tell it to, or that it actually deletes the Google stuff when I tell it to, or really much of anything about what it is doing or who it is talking to, so I still don't trust it - but I mistrust it slightly less, I suppose, than I would if the google apps were running.