This is partly something I've been thinking about for a while, and also inspired by recent posts in the Shin Eva Official social media thread about both i) the purpose of the time-skip between 2.0 and Q and ii) Anno's desire to see different interpretations of Eva, like with Gundam.

The references to Nadia in Q have been well discussed- Misato and Akagi, the Wunder launch sequence, NERV hq as a inverted pyramid atop a column, as well as music taken from Nadia, but Q and Final mark more than just references, but a fundamental shift in Eva's structure, from the classic Mazinger-like 'weekly monsters attack the advanced research facility where the robots are based' to the structure of shows like Nadia, the Solo ship in Ideon, Macross, Space Battleship Yamato (Misato's desire to see 'the red oceans turned blue again' and de-coreification are a lot like the Cosmo Cleaner from the first series of Yamato) or the White Base and Argama in the original UC Gundam series- where the protagonists are in command of a ship, fitting a series of running battles and exploring vs a more traditional set of antagonists- all shows either Anno has worked on or cited as major influences.

If you wanted to reinvent Eva, a way that would be both radical but also 'classical' would be to transpose it's setting or series 'scheme' to one like these classic ship-journey anime. Plus Anno really, really likes ships.

I can see where you're coming from with this, definitely. Anno is a huge nerd for all sorts of stuff, and we know for a fact that he has seen most of these, so it wouldn't surprise me at all if he did something of the sort.
Although I personally feel like that if Anno were to do something like it, it would tonally fall less into the traditional "road trip in a warship" storyline, and moreakin to something like Gundam 00 or Knights of Sidonia that emphasizes the vast loneliness of space over the prospect of going somewhere specific with the ship