I would absolutely get orthodontic treatment again, only this time I would have it done correctly. The first time you had braces you may have ended up with straight teeth, but you never addressed the much more serious (and aesthetically important) issue of your jaw to jaw discrepancy problem....
While the answer is "yes", you should know that the durability will be in question. Also, the space may be closed, but the size and shape of the teeth will be out of proportion. It may be worth having a cosmetic dentist make a diagnostic wax up and create a temporary or "trial smile"...
I have an orthodontic practice that sees about 25-30% adults. A large percentage of those patients are people who had braces already as children and thought that they no longer needed a retainer after several years. There was a large study done at the University of Washington that...