I am well aware of the reason all of the authorized Portkeys have to look like garbage (Why are portkeys always made of rubbish?), but what I don't understand is why they can't be mass-produced.
Let me explain: it would be much simpler if the Ministry of Magic were to make some kind of unique object to be a Portkey. This Portkey could be easily enchanted to go somewhere at a specific time or whenever touched, like the one to the Quidditch World Cup and the Triwizard Cup. Then, they could put a simple Muggle-repelling charm on it, like the ones for the Quidditch stadium or for Hogwarts, and just duplicate them again and again. The Muggle-repelling and Portkey charm would stay on these Portkeys (just as the burning charm stayed on Hufflepuff's cup) and they would be much easier to find and use for wizards. This would also avoid the possibility of Muggles' memories having to be modified.