I’m a little surprised to hear this is a new problem. If you turn WiFi off on the G4, do you see any letters next to the cell strength indicator (for example, LTE, E or X).
Meanwhile, please allow me to provide context regarding Republic’s coverage options for its newer phones like your Moto G4. Republic provisions cellular coverage with one of two network partners. One partner operates a GSM network and is T-Mobile. Republic’s other partner operates a CDMA network and is the now T-Mobile owned Sprint. Cellular coverage is provisioned with one network or the other not both simultaneously.
In your area, GSM coverage is weak. Much of it is “fair” signal strength. T-Mobile describes fair coverage thusly: “Cell reception outdoors and occasionally indoors”. CDMA coverage is, according to the maps, considerably more robust. That would seem to be confirmed by the fact your Moto X1 is not sharing the experience. The Moto X1 like all legacy Republic phones (Moto E1, E2, G1, G3, X1 and X2) is provisioned with CDMA (Sprint network) coverage.
It’s possible to switch the G4 to CDMA coverage. I’m asking about what you see next to the cell strength indicator with WiFi off to see what, if anything, might be possible in terms of improving the GSM experience.