The supreme court has numerous times affirmed limits to free speech. For example, the espionage act has been ruled constitutional. Military officers are prohibited from releasing classified information. You're in trouble if you call in a bomb threat.

You segue onto hate speech and drawing lines; this seems irrelevant here.

Were a Lockheed Martin worker to send the plans for the F-35 to China, they'd be put in prison.

Were Intel transmit the designs for that supercomputer that Intel weren't allowed to build in China to get around export regs, they'd be put in prison.

If it were the case that the constitution allowed the government to (say) prohibit the exporting of certain military hardware (say, a nuclear bomb), but not prohibiting the export of an incredibly detailed document explaining every nuance, datum, etc of producing that same piece of military hardware, I'd argue that the constitution needed a brief update (perhaps as you mention to 'shall make not many laws'). To my knowledge, it does not.

Then either this case will lead to failure, or success by arguing that any export regs on ideas are unconstitutional (thus leading to the bizarre problem above) or a success by proving that the export regs do not, or should not cover what he has produced.