The Zeitwerk servicing is something like 2,500 euros. If you can save much more than that, then it makes sense to go gray.
The only reason to buy from an AD is if you want the more desirable pieces down the road. Regardless of what they tell you, Lange has a list. You’re just not on the list, and the Zeitwerk isn’t that hot, that’s all.
This section has a good list of brands. I’m partial to Ressence, although there are many even smaller watchmakers at this price range.