Harriman wasn't a robber-baron, he was a hustler. A conman with principles if you like. Witness him convincing two soda companies (obviously meant to be cola and pepsi) that their rival was about to sponsor him to write their brand name across the face of the moon. So they'd each pay him to do no such thing.

Branson is no hustler, and Bezos is just a straight up shark. Branson would solicit sponsorship from whomever could pay the most, and Bezos would take both companies money and then renege on the deal and sic his lawyers on them.

I counter-propose that the closest we have to Harriman is actually Elon Musk. He has that element of showmanship that neither of the other two have, but he also has no need for anyone else's money to get where he's going... which btw, is lot more ambitious than anyone else, including Harriman! He's proposing to single-handily (well, him and his company) build all of the necessary infrastructure to successfully colonise Mars. Even Harriman only aimed for a privately funded version of an apollo moon-shot, not building a million strong city on Mars.