I am employed via W-2 and bound to a non-compete agreement stating that I cannot be paid for work outside of said W-2 employment.
Is it a breach of contract to perform work on behalf of an LLC which I own 100%, where payment is received by the LLC and not me personally?
Yes it is a breach of contract. Your LLC will not limit your non-compete liability.
There is a matching case: Gilford Motor Co Ltd v Horne [1933] Ch 935.
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.
On the face of it the non-compete only prohibits paid employment, if you work for free that would be OK.
That means that you must not benefit financially in any way from the work. You are proposing that the work you do will increase the profits of a company you have proprietorship of - this would be a clear benefit to you and prohibited.
