I'd have thought that the phone would have something to do with the relay of messages, out of range and the messages probably wouldn't be forwarded.
Telstra had an app called Text Buddy, worked very well and allowed sending of texts using your mobile number. Not sure why, but they withdrew it from distribution some time ago.
We still use it at work, I think I might still have a copy of the executable floating around which might give you a part solution (not sure but you may need to register your number).
Re the poor reception, I have the same problem at the shack. I bought a 13dBi yagi, went from no signal to 3/4 bars, needs an antenna connector on the phone though. I believe that there are "passive" cradles that can couple signal to the handset from an external antenna. Might be worth investigating.
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