Gurkenglas comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong Discussion
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A trifling amount of money by muggle standards, even if he didn't have the arbitrage trick, or the ability to make arbitrarily large amounts of money using the time-turner on FX markets.
He doesn't have to explain where the money came from, and the tricks you named require starting capital.
It was also unclear to me that Harry could take enough gold from the wizard economy to wind up with 100,000 galleons (even in sickles) without someone noticing and perhaps interfering. And that ignores the problem of leaving Hogwarts.