I suspect that places that do not reasoned to requests are already fully booked. Not too surprising.
Where are you planning to be for the actual fireworks? Piazza San Marco, or elsewhere? As I understand it, entry into the piazza is limited and they cut it off at some point, before it becomes dangerously crowded. It might be better to plan to watch elsewhere, and thus have dinner somewhere away from San Marco itself.
I have read that the fireworks are set off from a pontoon anchored just off the island of San Giorgio. That means you should be able to see them from places in Dorsoduro and Giudecca as well; even from Lido as one blog recommends (but it is a distant view).
I can recommend a Dorsoduro restaurant where our family had a wonderful dinner last October; it is an easy walk from the south end of the Accademia Bridge:
https://www.ristorantesantrovaso.it/
Not to be confused with Taverna San Trovaso, which at one time was a “Rick’s rec” but apparently is no longer. That one is more casual, very touristy, and not as good. The Ristortante has a special menu for NYT but not a pricy set menu. You cannot reserve directly on the website but you can enter a request.
After dinner, wander out toward the tip of the peninsula, know as Punta del Dogana, and hopefully find a good spot from which to view the fireworks. If there is no room at the actual point, the sideway lining the south side of the Dorsoduro peninsula is wide and offers more viewing opportunities.