Hi, Neil...
There is a Stammkennzeichen database available to all at the undernoted link:
http://www.luftwaffe-experten.org/stammkennzeichen.html
Unfortunately, I have checked under the 'T's and your machine isn't listed, but now that you have a Werk Nr, Stammkennzeichen and unit codes and details, you could always drop them an e-mail and ask them to enter an update to the records. It's not a complete record of every Stammkennzeichen, and there are still many to match up, but your contribution would be very much appreciated, and the kind that helps to keep things up to date.
Kindest regards...
