You can do it, and many people have done so...but it's illegal as hell. Federally illegal as hell, too. It's been covered many, many, many times already.
Simple solution: spend about a hundred bucks on an aftermarket cat, and keep your sensors where they're supposed to be. It's honestly the easiest, most direct fix for your problem. It's cheaper than what you were quoted (by a long shot), it's environmentally friendly, and it's not going to cause you to get fined if you get caught.
If it's worth doing, then it's worth over
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