I phoned Swatch in Aus. Very quick and clean. On it's way to me next week. I have never experienced the long delays that I get when I order via a repairer - stumped on why that is!
Not all that hard to imagine really. When you get a part like this through your repairer, they are likely ordering from someone else - it's unlikely that they would keep something like this in stock - stock costs money to keep and this would be a slow moving part for sure.
They are not likely going to drop everything and order just your one single part from Omega. They will accumulate orders until they have enough to justify the time and shipping costs of getting parts in from the supplier. How often they order will depend on how many parts they typically buy from that supplier - for me I order from Omega at least once a week, often more than that, but certainly not everyone would do so.
Also consider if they are ordering through some other third party, like a material supplier you see mentioned here (Otto Frei, Cousins, etc.). If it's from a place like this, you can add yet another layer of delays while that company gets enough parts for an order from the actual supplier.
Also note sometimes the in country or local branch of Swatch/Omega will not have the part on hand, and it has to come from Switzerland. Your local branch does the same thing again - they order once a week from the mother ship, so depending on the day the order gets placed, it can be more than a week before the order to Switzerland gets placed, and then the parts usually take 2-3 weeks to get to your country headquarters from Omega in Switzerland.
It all adds up, and if you happen to hit all these delays at once, it will take a long time. You got lucky that the part in question was in stock in your local country, otherwise it would be at least 2-3 weeks.
Cheers, Al