1. Do nothing,
2. Ask them to stop again (politely, with or without warning about going to authorities),
3. Ask them to stop again (not politely, with or without warning about going to authorities), and
4. Go straight to the authorities.
My recommendation? Go straight to the authorities. You've been polite, and you do not deserve to suffer as they benefit. Make no mistake, the only reason they are doing AirBNB is to profit. You have every right not to suffer a 'diminished quality of life' (as you, very succinctly I must say, put it) just so they can put an extra, what...$30 a day(?) in their pocket.
Strictly speaking, anyone operating an AirBNB rental is operating a business. They are providing a service/resource to those who are willing to pay. Is an expense to that business paying the people around him to allow him to do so? Maybe (we as a society seem to endorse the idea of a 'money to QoL' ratio). So, my next question is this: is Mr. Ignorant claiming that income on his income tax? I imagine not. That might be more legal leverage you have in this case. (Side note: little do most people know that if you legitimize a business, a huge array of tax incentives start rolling in (proportionally expense your Internet, heating, electricity, computers, vehicle, etc).
I wish you the best of luck in your quest.