Hey, Lu!
Afraid you will have to pay the extended permit fee.
As with all things in life, there's more...
I hit 120 days the beginning of Dec. 2020 and was blocked from booking ANYTHING (even nights in 2021) for all of December, figuring, "what the Hell, deal with it next year," right?
Then, I get the Airbnb tax breakdown notification and, thoughtlessly go and take a look. There I notice: "Total days booked, 2020: 87" Oddly, if they were counting 2021, I was able to book again Jan 1. Water under the bridge at that point but knowing I'll be hitting the 120 cap soon this year (2021) I have begun the process.
It took me all of 20 minutes to get to the point where the City would determine if I were "eligible" for the extended stay permit and once there, I've waited close to three weeks for an answer so I could proceed to the notification portion of the permitting process. Two emails, two voicemail messages to the city and nothing yet. Oh, and guess who's now 7 days from the 120 mark (Airbnb's math - I haven't counted).
Anyhow, that's my extended permit saga. Hopefully it'll be resolved soon - stay in touch; sounds like we're going through a lot of the same growing pains.
The per night fee Airbnb collects and remits for us so you don't have to worry about those emails.
Good luck, talk soon.
-Eric