Petra is a stunning place to explore. It's been made famous by movies, and the crowds you see there reflect that. The best way to escape the crowds and have a personal experience at Petra (if that's possible), is to arrive early in the morning. Get there right when it opens, and then enjoy a few moments of solitude. Pack yourself a lunch so you can spend the whole day there. Then head back towards the back of the grounds. There are a few hikes, some more difficult than others, that will take you away from the tour groups. Petra is so much more than the Treasury. By getting there early, taking the time to do some good hikes, and spend a day or two there, you'll get to experience it all. After all, you did go all the way to Jordan.