Hmm. That is the page I read. To be honest... I understand the Heap. stack stuff, but then just got lost. Beyond me.
I certainly don't understand how to replace my current code with something other than Strings.
My phone numbers for example.
They are read from 12x EEPROM addresses at the start of the code and put into the Users phone number String.
They can only be changed for a digit 0-9 in the users setup routine (which will very rarely be accessed - you only set your phone number once) and then written back to the same EEPROM address.
From then on, they are only ever recalled once at the boot to create the initial String. Is that going to cause an issue? They are not constantly changed.
I might throw this over to a Teensy, where I have more memory anyway.
I might have a go at changing the GSM code, but I just had a go and it didn't go well 
Below is a snippet of the code. This part if anything is more likely to cause issues, as it's reading data from the GSM module:
String GSM_readSerial() {
GSM_timeout = 0;
while (!GSMSerial.available() && GSM_timeout < 12000 )
{
delay(13);
GSM_timeout++;
}
if (GSMSerial.available()) {
return GSMSerial.readString();
}
}
:o Never as simple as I think