Good advice, thanks. Suffered the same problem with my 2012 A6 Avant. Did as you suggested (getting the trim off was the hardest part - 4 screws to remove before springing off the clips), the motor looked in my the same state. Cleaned it all out and re-greased it. Couldn't really see how the water connection on the back plate could fail to leak inside - anyway I put loads of grease around the end of the spindle there so perhaps that will help. Delighted that it seems to work normally now - saved a bundle of money.
Incidentally there seem to be a lot of new motors available online for £35-£40, fitting many Audi models but not the A6 from 2012 onwards. The units in the photos look exactly the same as mine.