I think you are overthinking it.
Powerful / rich men have always seen access to women as one of their rights. It's only in the last twenty years or so that society has recognised that older men having sex with teenage girls is abusive even if she believes it was her choice because of the power difference and likelihood of grooming. Most of Epstein's crowd grew up before then.
So it's not so much that they didn't think they'd get caught, as that they genuinely didn't think it was a big deal. In their heads they were James Bonds on their island surrounded by bits of pretty fluff. Hence Mandelson, a gay man, still enjoyed it because of what it represented - success and power.
They saw themselves as important and the girls as disposable beause that is how it has always been, and they assumed society would too.
And frankly, they were and are probably right. I'm sure even now, behind closed doors a lot of the (male) media and political establishment feel it's a storm in a teacup and resent being forced to do anything about it.