Yes, if a loose fit were the cause, 5th would also be a noise concern. However, the loose fit of the OD spool gear is more attributable to a vibration. A vibration that may also come with a whine/ light mesh noise.
If its just noise, I think the isolation, or lack there of, is the cause. The fact its more / only in 6th may be due to the 6th mesh being closer to ( right under) the shifter housing. Add a thin rubber sheet between the shifter stem and the stick ( if there is a joint- later B&M s don't have them) also, check for a torn body to shifter boot as well.