I would definitely look at airb2b and homeaway and agree to expand the search.
Each of the 5 towns is so tiny and Vernazza smaller than Riomaggiore or Monterosso so options are limited to start with.
Finding large places that also have a sea view terrace in the town will be hard, just don't think many exist in Vernazza.
I think that could be found without too much difficulty a little up the hill from the town in Vernazza or if you are willing to look at all of the villages and have a little walk. Or stay in heart of Vernazza but lose the terrace requirement.
Always a good idea to look at the bigger folks like booking to see what is available and then you can google for individual websites or listings by owner of the same property listed on booking and reach out to them via email directly.
Booking in particular has some apartments and houses now, they are not just hotels and B&B's.
Going in Sept myself and wanted a sea view balcony room in Vernazza for 3 people (2 adults and young child) and found virtually nothing when I looked and booked 10 months out, so think it is more about what actually exists vs. everything is booked. I found places for 2 but not for 3 or 4. I originally choose a sea view room by the tower in Vernazza (windows but not balcony) at more of a hotel type place but since cancelled that for a studio right in town by the train station without a view as I decided the added hassle of all of the stairs and accessing the room was not worth the benefit of the view from the room. Would rather have easy access to the room from the town and the train station.