There's nothing in your posts to indicate that this has anything to do with the complexity of the movement. The 3606 is pretty much the same as the 1151, which is pretty much the same as the ETA 7751. There is nothing special about them in terms of challenges for a watchmaker. As I've said many times, the 7750 series is the one movement that if I have it on my bench, I know the chances of it being a trouble free service are very high. Having said that I have a 7753 on my bench right now that is worn out completely, and is being a complete pain in my arse...but that's another story...
So a few things I want to mention, just to give you some perspective/information that Omega isn't giving you:
1 - The fitting of dials, hands, and the final casing of the movement is not typically done by a trained watchmaker at the service centers. This work (as well as the steps in reverse when the watch first comes in) are done by people that Omega have hired off the street, and trained specifically for these tasks. The actual watchmaker would typically only service the actual movement, and others do the rest. This also applies to the refinishing of the case. I've been to the NJ service center for training and the people who refinish cases, that's all they do - they are again not watchmakers but people trained specifically to refinish cases.
2 - Although the dial may have seemed "pristine" to you, note that as part of the job to assess the parts, if even a small amount of finish is able to be flaked off the edge of the dial (where you would not see it) during the assessment the dial would be considered a required replacement. Also since you are unable to see the condition of the dial feet (the posts that are used to attach the dial to the movement) there's a chance that the dial had a post that was either broken off or nearly broken off. So although to someone not familiar with watches and how they are repaired might find it odd that a dial suddenly needs replacing, to me it's not particularly surprising.
3 - When I order parts from Omega, if the parts are in stock at the Canadian headquarters, I can have them in my shop the following day if I order in the morning. However if they are not in stock and have to come from Switzerland, then all bets are off. First I suspect just like the Canadian headquarters does, the NJ service center would order parts once a week from Switzerland, so if your damaged dial was discovered the day
after that weekly order gets placed, it waits a week until the next order is placed. Then delivery to headquarters takes 2-3 weeks - it's just the way it is. Note that on occasion (thankfully not very often) I have had items that even the HQ in Switzerland doesn't have on hand, and in that case the delay is even longer, so that is certainly possible with this dial or some other part they require.
4 - When the dial arrives it has to be installed, the hands installed, the movement cased, the watch pressure tested, and then it's run through a series of QC/timing checks, including a power reserve check. So the watch doesn't get shipped back right away when the work is done. My own QC procedure lasts at least 10 days, and although Omega's isn't that long it does take time.
Now just my own thoughts on your situation - I understand this is frustrating, but I think once the watch is back and working properly (fingers crossed!) the delays you have experienced will quickly fade away. It seems like a lot now, but really in the big picture it's not, and honestly I don't think pushing harder on Omega is going to give you a better outcome - the last thing you want is them rushing through this IMO. Maybe once it comes back ask for some type of compensation - some Omega swag or something.
Cheers, Al