Regulation of international commerce grants the federal government the right to determine what commodities, and labor is a commodity, enter the country. That would be one constitutional bar to a contract with an illegal alien.

Further, contracting with an illegal alien is aiding and abetting his violation of the law, making the contract itself illegal no matter that you have a right to contract with whomever you desire. This was once exploited (is probably still exploited in some instances) by unscrupulous employers in this country -- they would contract for a season of labor, and then call immigration authorities to arrest the illegals at the end of the season, refusing to pay them on the grounds that the contract between them was invalid. It was the idea of targeting the employers, done in reverse by the employers. Citizens don't have a right to enter into illegal contracts.

So there is no infringement on a born citizens right to enter into a legal contract, but they are barred by law from entering an illegal one, just as they have been since the Constitution was first written.

Your point that immigration and naturalization makes no one an originalist would be very interesting, if it were correct. The court cases I cited basically mean your view isn't correct.