Had he approached Padma in a friendly manner, putting himself on equal footing (instead of trying to teach and impress!), and then told her pretty much the same things he ghost-whispered, it would still have likely redeemed her,

Personally, I disagree. When I imagine Harry approaching Padma with such a strategy, I see Padma reacting to his attempt to understand her with revulsion and self-justifying lies to minimize cognitive dissonance, thereby pushing her even further from being able to admit to herself the truth of what he says.

The ghost gambit works because, like an anonymous comment, she can't employ a cached thought like 'everything Harry says is evil and intended to manipulate me and false' and reject it out of hand, and she is rendered weak and uncertain in a way independent of Harry. Nor can she overrule her cognitive dissonance by focusing anger on Harry for manipulating her - because she has very strong evidence that it isn't Harry manipulating her.*

But perhaps I am too cynical.

* Yes, we know that Harry did it and that he obviously did it because of his invisibility cloak. But she doesn't know about the cloak, and given the enormous unlikelihood of Harry having such a cloak and a Time-turner, I don't think she is wrong to conclude it wasn't Harry.