An adherent of "originalism" would have supported Lessig in the Eldred case; your "original" view is at odds with the understanding of copyright at the time of the Constitution, yet oddly consistent with the understanding of copyright by the RIAA and MPAA.
More importantly, your objection is ridiculous. Of course Congress has ample authority to regulate copyright. That doesn't mean unfettered authority to impose excessive punitive damages in civil cases in violation of the due process clause.
You act like a clash of constitutional clauses has never occurred in the history of the Republic. The constitution was designed with "checks and balances," a phrase you may have heard before. The bill of rights (including the due process clause) is a check on the powers of the government (including to regulate copyright).