Sigh. I can't believe there isn't a way to get Stonehenge a turn faster.
I don't have an answer for you (I wish I did since I'd love to test things out and using developer cheats is the fastest method) but

this one made me laugh
I just don't get how it works. Your people spend centuries working on a Wonder, and because someone on the other side of the planet finishes it first, it becomes worthless?
5 minutes faster and you have a beautiful Wonder that helps your empire flourish, 5 minutes slower and centuries of hard work gets you maybe enough spare change for a Big Mac?
If someone beats you to a Wonder within so few turns, you should both get the benefits. If it's a few more turns, maybe you get a lesser Wonder with lesser benefits, or at least some buildings in your cities of the same hammer-value.
But really, whenever I lose out on a Wonder I look at what happened and just try to do it differently the next time.
Really? You start a game, pour everything you have into a Wonder, and then you're satisfied with a few bucks? You keep playing a game where your neighbours all have the units and buildings they spent their time building, while you sit there with nothing but a few bucks to show for your opening millenia?
Or just go take the city that built Stonehenge.
That's my usual strategy, but I don't know where that is. Plus, I'd have had to spend the time building units instead of wasting my time building something that would get me a few bucks.
Chopping a couple forests is probably the easiest way speed up the production by a few turns. I will cost you production per turn later, but will speed up your wonder.
Yeah I'm playing on Marathon so I'd have to go way back to move my worker to my lone forest and chop it. That would mean having to re-explore all the land I've already explored.
That being said you'll probably learn more if you learn how to play without reloading. Once I stopped using exploits like that and started focusing on learning better strategies I was able to jump up a few difficulty levels and still win easily.
In fairness this is obviously one of my first games of Civ 5. And in fairness, missing out on an early-game Wonder by 1 turn is a rather unusual and BS situation.
The only thing you'd really "learn" is to avoid building early-game Wonders.
And I'm not really one of those guys trying to develop (or follow) a system, I just play for fun. And in this particular game I wanted Stonehenge and lost out by 1 turn.
Bring back WorldBuilder!