Never noticed gear whine on my old NT, but the DR650 has a real loud 3rd gear whine. Tried a couple different types of oil when it was newer and it didn't seem to make a difference in noise.
I have used Rotella T6 5w40 in TU250, DR650, and NT without issue. The DR650 has shorter oil change intervals than the NT. On my big trip I let the T6 sit in there for 4000 miles, which was 1000 miles longer than I normally leave it in there. I wasn't worried at all about it not protecting the engine. I bought some Castrol synthetic 4T 10w40 for the new tiger but I plan on going back to Rotella T6 when all the expensive castrol is gone.
It may have been mentioned already but Rotella T6 has the JASO MA symbol that certifies it is okay for use in motorcycles with wet clutches. I started using the T6 after on the NT after it crossed 4,000 miles. I know that a bike will often shift better after a fresh oil change, but I remember being impressed with how smoothly it shifted the first time I rode it with T6. It was then the only oil that my I put in the NT after that. I always had more than one bike, so I rarely did more then 6K a year on the NT so I just changed it annually at the beginning of spring.