It is actually very common to see a large discrepancy between the practice tests and the real exam, but only in one direction--down!

Does this mean the practice tests are easier? Not at all. It means that taking a practice test is less likely to go wrong than taking the real thing. Here are a few common problems:
*You've seen some of the practice material before. This creates more score inflation than most people are willing to admit! However, it looks like you didn't repeat any tests, so this probably isn't the case for you.
*You give yourself an advantage on the practice test that you don't get on test day. (Longer breaks, pause button, breaking up the exam, skipping essay or IR, etc.) In your case, as angelfire points out, this seems to be the culprit. Why are you giving yourself these advantages? You don't get to keep those practice scores!

Let me give you some blunt advice:
never practice this way again. Practice tests are meant to simulate the test, and you have now wasted all of the best tests available without actually having that experience. If you want to do untimed review, do that after. Even with individual OG problems, you should get used to doing them under timed conditions first.
*You are more comfortable and less stressed taking a practice test at home. You can address this in a few ways--first, by taking the exam away from home (e.g. in a library), and second, by pretending that you are taking the real test. As much as possible, the goal is to blur the boundary between practice and performance. It's the same thing you might do if you were playing guitar in a band. At home, you motivate yourself by saying "Okay, everyone's waiting for my big solo!" Then on stage, you might combat nervousness by saying "Alright, it's just another practice day. Let me play it the way I've been doing at home."
*You changed something about your practice on test day. This is closely related to the last point, and it may be the biggest factor in bringing people's scores down on the real test. If you tell yourself "Okay, today is the day I hit 760!" you may be setting yourself up for disaster, because you're not used to performing at that level. Putting too much pressure to succeed makes you more anxious and less able to think, and it also makes you more likely to stubbornly persist on a problem when you should guess and move on. I can't tell you how many times a student has told me a story like this: "My highest practice score was a 650. I really wanted a 700, but I got a 590." Why does this happen? Because when you say "Today is the day I'm going to do better than ever before," it actually doesn't help. You just want to recreate your home performance.
So in short, look for the differences between home and the real thing and eliminate them systematically. Whether it's one of the above or sleep or nutrition, take the necessary steps to make sure that your practice tests run just like test day will. Then walk into the test center and do it all the same way. Honestly, if you are hitting 660 on the real tests, it is probably because you are at 660 level. To improve to 720+, you will need to do some more study/review, but you may get a bit of a boost simply by getting used to the entire 4-hour endurance event that is the GMAT! Good luck!