I'll start by saying (at the risk of excommunication) that all this talk of phonetic systems is ridiculous.
Some of the principles are based on specific phonetics, like r-e-t-e-n for return *DJS* - but I don't say the word that way. But I still write it that way.
And I know a guy from Australia whose name is Dale. He says it dial. But I still would write it d-a-l. And likely so would an Australian Gregg writer. No?
And the only way to learn to write fast is to pick an outline -- preferrably the one in the dictionary -- and keep writing it until you learn it.
So, while some of the principles are phonetically based, I believe Gregg has its own spelling -- for each version -- that we should stick to if we want to be competent.
Bwa-ha-ha