In practice, the conduct you describe is almost sure to be found to be a breach of the non-compete. You are still doing competing work employed when employed by another. You are also receiving all economic benefit that arises from that arrangement. Even if your violation didn't violate the express terms of the agreement, you would probably be held liable for acting in bad faith to circumvent the agreement.
Of course, all of that assumes that the underlying non-compete is itself enforceable at all. Many states, e.g. California, are legally very hostile to non-compete agreements and decline to enforce them on public policy grounds absent some very specific conditions. But, if the underlying non-compete would be valid if you went to work as a W-2 employee for a competitor, you are almost surely in breach in the scenario you suggest.