My question involves landlord-tenant law in the State of: New York City

Tenant here. Long story short:
1. I live in a basement or cellar apartment with 1 roommate
2. For months we notified landlord of mouse droppings, asked for exterminator to take care of roaches.
3. Finally, rodent ate through packaging of my stored food.
4. After months of problem not being solved, I emailed landlord. Paraphrased, "we made a good faith effort to resolve this on our own. We did this, this, and that on our own. Pursuant to NYC Warranty of Habitability laws, can you please seek immediate resolution to this?"
5. 1 week later, receive a "Notice to Vacate" email. Landlord is now requesting me to move by September 31st.
6. Landlord is already advertising same apartment online available for occupancy October 1 for 19% increase over what I pay

Pursuant to New York Real Property Law 223-b, this seems like a retaliatory eviction.

The trouble is, I didn't even file an official complaint through 311 or do it myself online.
223-b 5 a: good faith complaint not made to a "governmental authority"
223-b 5 b: I didn't commence an "action or proceeding in a court or administrative body of competent jurisdiction"
So the only proof I have is my email with reference to the words, "warranty of habitability". Then a week later LL's "notice to vacate" email

This building may also fail to meet 223-b 6, since this is an owner occupied dwelling with less than 4 units. Department of Finance records state this building is 3 units, 3 stories. (There are a total of 8 room rentals).

I just need some clarity. Do I have a leg to stand on with the Retaliatory Eviction defense? Thanks!