After fixing the setup, the measurement with the new disk looks great. After more than one hour the first two modes are still ringing down, meaning that the Q's are larger than 10 millions.
Here's the comparison of the spectrum before and after the excitation, with the identified modes:
I used about 4200 s of data to fit the ring downs. Most fits are good. In a couple of cases the peak splitting is large and the algorithm fails to fit the beats:
In summary, here are the Q values for all modes. Despite not being annealed, this disk shows very large Q's