Dude, your Free Republic follows strange logic.
According to you, if something is given a nickname that becomes popular, it is assumed that the thing did not exist before it was given the nickname!
The word "Hindu" is a corruption of the word Sindhu (Indus river) by the Iranains who have no "H" sound in Persian language. It is just a nickname given by dudes living west of Indus river for dudes living east of it.
The word Hindus obviously doesn't occur in any of the "Hindu" sacred literature like Vedas, Upanishads, etc.
But did you ever pause to ask what the Hindus have always called themselves and their religion -- what is their "real" name, as opposed to the nickname "Hindu"?
The answer is "Sanatana Dharma". This means "Eternal Faith" and is the real name of the religion that Hindus follow and they call themselves "Santan Dharamees". This is the name that occurs in their sacred literature.
"apparently introduced by the Aryans is gleaned largely from the Vedas."
The Aryan invasino theory has been discredited as imagination of the 19th century Missionaries like Max Muller and modern day Indian communists. It has been abandoned by most historians, including American universities.
"Obviously it is not an established fact as to when the "Gita" was written much less called the Bhagavad Gita."
You know that Gita and Bhagvad Gita refer to the same text, don't you?
"It is very clear that there was and is no one religion called 'Hinduism' and what existed in 500 BC when the historical Buddha lived"
Santana Dharma existed for thousands of years before that, inclduing all its scriptures like Vedas and Gita and the two epics.
Sure, the nick-name "Hindu" did not exist as Persians had yet to discover India.
Got it?
Got it?