If it's any comfort, I'm trying to solve the very same issue. If you are able to resolve it please post back here.
Mine will receive them fine. It will send and receive SMS. I've played around with the APN and have no positive results there so reverted back to factory with them.
I've not tried any other keyboards other than the standard Google.
Might not be a problem with the moto but with the receiving phone. Mine sends okay to other phones, but not to Touchwiz devices. My 2013 G was able to do this while running 4.4.4, but not this newer G.