Stuff happens
Well, what I did was a clean install of Sierra, but I did not remove and re-pair the bluetooth devices (I use keyboard, Magic Mouse, and Bose qc35 headphones). Now I followed your advice and re-paired all devices, and rebooted (tricky since I had to dug up a wired keyboard and learn how to press onscreen buttons with spacebar! - Apple just works, isn't it? =)
All is well for now, but time will tell, since from my observation, bluetooth audio in Sierra works fine after reboot, but some time later the stuttering reappears. Fingers crossed and thank you for your suggestion. I still think Apple needs to do more thorough testing before shipping their "improvements"!