Without fault codes VW is unlikely to want to spend their money(I'm assuming you have a CPO warranty) on the problem unless you can demonstrate to their satisfaction that the transmission is severely flawed. As a start, I would let your dealer keep it overnight and drive it while it is dead cold. Hopefully it will replicate your concern for them. At this point you can discuss with them the options and what they will pay for and what you will be responsible for.
Since it shifts flawlessly when warm, I would doubt the transmission is toast. To me the options would be
1. Multiple drains of ATF fluid and a change of the filter.
2. New(rebuilt) mechatronic unit combined with number 1.
3. Entire new transmission(not likely?)
If you are under warranty it may be hard to get option 1 paid for. If it is option 2 or 3 and VW agrees, the warranty should cover it.
Michael changed his ATF fluid and filter on his W12 as a preventative measure. Maybe he can help you out a bit.
I had a 1988 BMW 750 with a 4 speed ZF transmission that did exactly what you describe for my entire 9 years of ownership. If it makes you feel better, it never got worse but it didn''t get better either. I didn't repair it since the car was so old and had almost 200k miles on it. However, your W12 deserves much better.