I’m afraid my experience in Tanzania may not be horribly helpful. I travelled almost two years ago and took with me my Republic Moto X 1st gen. This is a 1.0/2.0 phone that, while not officially “locked,” could not be used on any other carrier due to the custom ROM. As such, my network utilization in Tanzania - at least in the eyes of the Moto X - was entirely WiFi-based (I often tethered the Moto X to an iPhone 5S with a local Vodacom SIM). This arrangement meant that any local calls or texts on the Moto X had to be completed through a 3rd party app, Google Voice in my case, as Republic did not natively support outbound international calling or texting.
Fast forward a couple years and about a month ago I found myself with a Moto G4 in Peru. I really didn’t run into any problems activating it on a local carrier, Claro, and used it extensively for data and occasionally for local calls and texts. Of course, it wouldn’t send or receive calls on Republic (even over WiFi) once I had removed the RW GSM SIM card and installed the local one, but I also didn’t see any of the same headache you reference with messages going poof and disappearing into thin air.
I am thinking one of two things may be going on with your phone: either the phone is unsupported by the carrier or for whatever reason the phone is mixing up residual Republic configuration information with that needed by the new SIM. I travel a fairly decent bit internationally and while by no means a scientific study, have never run into the issue of an unlocked GSM-compatible phone not being supported by a local carrier. By no means is it impossible, I just haven’t run in to that yet. Regardless, even if the G4 N. America Unlocked is known to have issues on the local carrier these likely are not well documented.
I think it’s far more likely that you’re running in to some messiness associated with residual RW information causing problems with the local sim configuration. As @rolandh recommended, the first thing I’d recommend you do to try and combat this would be to uninstall the Republic app and restart the phone. Verify everything in Settings>Wireless & networks> Cellular networks makes sense; most everything should be set to automagic or it’s equivalent. If you’re able to go to a Halotel store (not just one of the recharge booths) it wouldn’t be a bad idea to have them look over the settings for you. Just be careful, in my experience at Claro in Tanzania (as well as at other similar establishments in Ghana on a prior trip), the prices changed from minute to minute and there was definitely a premium for foreigners (which can be gotten rid of with a bit of negotiating). If you’re still running into headache, I’d recommend a factory reset of the phone. This is a bit of a pain because of the time required to backup and restore everything but if there is in fact old RW information causing your issue this will almost certainly get rid of it. The other option (which could be tried at any point in this process) would of course be to purchase a Vodacom or other SIM (or borrow one) and see if it works properly on your phone.
Sorry for the thesis-length response and please let us know if you end up having any joy in getting it activated. I know that’s a lot of not-entirely-organized information - I’m running on fumes with about 50 lb of work on my desk to finish by tomorrow noon - so please let me know if there’s anything that doesn’t quite add up or you want me to do a better job explaining!