I assume that they'll have models that correct for all of that, and I assume they'll have satellite weather included for up-to-the-minute data on all of the factors involved. (Either that or I'm guessing wrong about the effects of those things.)
Assuming all of that... what kind of precision are we talking about? Can they hit a building? A tank?
I'd opt for many small fast ships with a small crew, and one or two guns, and just enough armor to keep them from being sunk by pirates, etc. There should be enough storage on board for about 1000 rounds for each gun. I don't know how fast hydroplanes are, but that's the kind of speed I'd shoot for... 100 knots, so you could be anywhere in the world within a week.
Battleships are romantic, but they are obsolete. You can't make armor thick enough to stop today's missiles.
Part of the problem is the F-35 lacking the range to compete with china and russia's fighters. While a 1000 mile range is impressive. The accuracy could not compete with the laser precision of guided munitions launched by aircraft. Significant disadvantages over the long term.