"What's deeply ironic is it's entirely possible that one or more of these billionaires is going to do more to solve these problems than all the government programs combined. "

I don't hold such a faith. I think these billionaire did more to "solve these problems" [hence they being the billionaire they are].

Branson lowered price of air fares and provided good service- cutting bureaucratic and general bullshit will result in lower CO2 emission.
If, Branson is major player in suborbital travel, in the short term there won't be any reduction in CO2 emission, but there could long term consequences which could do this. And this is true if we strictly limit it to just suborbital travel. If we expand it out to what means in terms future use of space environment- it could be MASSIVE in these terms.
But Branson isn't interested in suborbital travel because he wants to lower CO2, just as he didn't have this as major objective in his airline business.
His focus was on better service and lower costs- and if you lower costs one will lower CO2 emission- at least in terms of how much total CO2 is used to move a person from one location to another.