So you disagree with your own Greek Expert!
To say, “For by grace you have been saved, and that not of yourselves; it is the gift of God,” is a tautology. If it's by grace then obviously it's not of ourselves. So when Paul says, “For by grace you have been saved
through faith, and that not of yourselves; it is the gift of God,” it is those words 'through faith' which keep it from being a tautology. Therefore it must be, as Mounce says, the whole of salvation
including faith that is the gift of God.
I studied Greek for a number of years, but I am not any sort of expert to contradict Mounce, and I don't need to because he proves my point. However, I did take time to look up William Hendricksen's commentary of this verse. He spends four pages discussing it, so I won't paste all of it.
The problem is that the word 'that' is neuter in Greek, while 'salvation' and 'faith' are both feminine. So what does 'that' agree with? Hendricksen suggests that it is the
act of believing, which would be neuter which is represented by
touto. But whether one agrees with Mounce or Hendricksen, the fact is that the whole of salvation, every aspect of it, is of God.