Easy enough - each round, resolve each ship's movement and action(s) in turn but with the clear understanding that it's all happening at once.* Just because the shots from your ship happen to be resolved first at the table doesn't mean the target ship will sink before it can fire back: it too gets its shots in for the round, and maybe after that it sinks.The hardest thing for me, is how to capture the idea of simultaneous movement and not turn based movement.
Also, and again this is different from how normal D&D combat works, movement has to be seen as a continuous thing. In a normal D&D combat, movement often almost seems to work like a mini-teleport - you're here, and on your turn you're suddenly there, having spent no apparent in-game time to cover the distance. Can't do that with ships.
* - unlike a typical D&D combat; and D&D could really use a lot more simultaniety of resolution in its combat mechanics.
Still sounds too turn-based.One idea I liked from black seas is being able to fire on your opponents turn (almost like a 5e reaction) in exchange for not firing on your turn. There is a slight penalty to it but I really like that rule. They call it Fire as She Bears.