Until Google resolves the issue with Google Play services getting anything synced to your Google account on the Moto X would be a challenge. Contacts would be relatively easy, however, moving apps would require that each be individually sideloaded to the Moto X.
Have you opened a help ticket regarding the return of your Moto G4. If not, I suggest you do so when signed into your Republic account here: Republic Help. If you already have an open ticket, please comment on that rather than opening a new ticket. Republic is well aware of the dilemma caused by the Google Play services situation. I’m confident, they’ll work with you on the return window given the circumstances.
In an event, factory resetting the G4 won’t cause you to lose contacts or apps as those are synced to Google’s cloud and will sync back to the Moto X when the play services issue is resolved and you’re able to sign into your Google account on the phone. You may verify your contacts are safe here from a computer: contacts.google.com.