It seems to me that the genuinely interesting legal question about large-denomination platinum coin seigniorage isn't whether it's legal (it clearly is) it's whether it's mandatory.
1. Under the Congressional Budget and Impoundment Act of 1974 it's illegal for the president to spend less money than congress has appropriated—the Nixon administration had this idea that it could enact unilateral spending cuts, but it can't.
2. Under the terms of the statutory debt ceiling, the president can't borrow extra money without congressional authorization.
3. I don't believe there's a specific statutory prohibition on collecting taxes that congress hasn't authorized, but this principle is pretty literally the foundation of the entire fabric of common law.
4. The Treasury Secretary can instruct the mint to create platinum coins of any denomination.
On its face that leads to the conclusion that if the federal government's financing needs exceed its borrowing authority, the secretary must mint the coin. Many people have observed that it's difficult to see who would have standing to mount a legal challenge to the validity of the coin, but it's easy to see who would have standing to challenge failure to mint the coin—whoever didn't get paid. Say Obama implements a payment prioritization scheme and Obama just stops paying SNAP benefits. Well, there's going to be a whole bunch of pissed off poor families out there saying the administration is violating the Impoundment Act. The government must cough up the money. They will sue (I bet someone fancy would take the case pro bono, but if big grocery chains or Wal-Mart would help them hire counsel) and if the Solicitor General tries to say the government had "no choice" but to skip payments, the plaintiffs' attorney will argue that they did in fact have a choice—they could have minted a large denomination platinum coin.
Is an answer like "well that sounds silly and besides, members of congress who wrote the law probably didn't mean for it to be used in this way" going to be an adequate rejoinder to the plain text of the law? I'm not a lawyer, but I don't see how it could be.
One possibility is that courts could hold that the Impoundment Act is unconstitutional. But it's important to understand the implications of this. You'd avoid the platinum coin only by vastly increasing presidential power, and granting the executive branch authority to undo acts of congress unilaterally.