Hi Sony Slave,
I have listened carefully to three types of 6AV6 tubes with the box getter; RCA, Tung Sol and Sylvania.
It seems to me that the RCAs are excellent, but the Sylvania with a clear top, a little dish on top of the plate, side getter, and box top are even better. Here is a picture:
Now, burning in the amp itself, burning in headphones, speakers, and burning in tubes, require a signal. In the olden days you could buy CDs with a burn in signal that comprised all frequencies in a sweep. I would just leave the track on repeat, leave the volume on low, close the door and leave it overnight for a few nights.
Another suggestion is to use FM "white noise" which is what you hear between stations.
Here is a link to white noise, pink noise and something new to me: brown noise.
My guess is that most mechanical and electronic things improve after a burn in/use period. Just think of a new car, or a new pair of shoes or a new chair - they all function better after being used!
The 6AV6 tubes come into full bloom first after some 50 hours of burn in, and the change is dramatic.