Need some more information here. Above a truss rod adjustment was mentioned, but in which direction (or even if) is largely depending on where the strings are buzzing. Is the buzzing all around the fretboard, only on certain strings, etc... When I received my second hand HBII, I needed to loosen the truss rod because it was buzzing ONLY from the 1st-5th frets on nearly all of the strings.
If could be that by dropping the tuning that little bit, you may need to raise the action a hair to compensate for the looser strings. Heck, it could also be that your nut slots are too low, which means raising the action might not necessarily help.
What's the action currently like on the guitar?
Just in case, here's a great link to some setup resources:
https://www.sweetwater.com/sweetcare/articles/guitar-setup-part-2-setting-action/