Whine in a spiral bevel set is almost always from contact pattern. A bad contact pattern may come from too much backlash, but the pattern is the key.
see pg 18 of
http://www.arrowgear.com/pdf_files/catalog.pdf
Take the suggestions and double check yourself, or bring it to a reputable shop. I've found that a lot of times a local drag racer will be better than a "mechanic" shop.