The issue is, I don't see NRx providing a clear difference between monarchy and modern demotic dictatorship, and clear ways of preventing the first from sliding into the second.

For starters a monarch doesn't have to spend most of his effort manufacturing democratic support, thus he can actually focus his effort into governing the country.

That doesn't explain the difference between a monarch and a dictator, as requested. Once a dictator has suspended elections, they don't need democratic support either.

Under a demotic dictatorship, all people are required to participate in politics and form their own political opinions, and those opinions had better mach the dictator's/today's cathedral consensus.

That means that means that they have less time, not that the dictator does. The dictator doesn't need to manufacture assent, they rather need to quash dissent...as would a monarch, as many did. NRxs just assume that Monarchy will work effortlessly, because that's their desired conclusion.