There should be no need to scale anything by mapsize, because the mapsize is not a scale factor, it's an actual size.
The trouble is how speed and oversea mobility run into each other in the game with turn-based play. I would go so far as to say that a game with 1 movement stat cannot have balanced sea warfare period.
You need to take a page from the air combat system to have ships work. Early on, those techs increase movement to facilitate exploring the oceans and indicate ships that can rebase and float wherever they want. But everything after 6 movement overwhelms the positional grid system itself because of turns.
You have some tools because you have some freedoms to treat later naval developments different from earlier ones. The bonus to oversea movement can be understated because it just doesn't impact exploration anymore, but instead just relocation. And the stat, in that sense, should grow sublinearly. The extremes of movement overwhelm the sight radii of units, but movement can be treated as an enhancement to sight radius, with scouting and such - you have enough mobility to look around and still travel. And movement vs. sight radius is an appropriate arms race that will keep things interesting.
Lastly, though this would be some ambitious reprogramming, ships need to have the ability to control their surroundings from other ships, that's like... literally what they do, but again the turns are interfering. It has to be ships that do this, not owned territory. Some simple methods are ill-advised: Implementing zone of control is especially inappropriate for ships because of size and remoteness. And you can't have an interception mission, that completely warps sea's difference from aircraft. Ships are about being moving in the right place at the right time, creating passages and lanes. So ships should have a patrol option, and what it should do is allow the unit to literally occupy more than one tile. By expending its great surplus of moves to do that, it can cover an area by indicating that it is freely and fastly patrolling great spans of the water during the time period represented by the turn (specifically, the other guy's turn where he sails his guys up through your stuff at 10 tiles a time). This creates an appropriate defense to mobility paid for with mobility, so the arms race exists, but fair for the swapping of turns.
In the same line, just as mobility becomes this bonus action of patrolling at the extreme upper end, the bonus sight, after a few quick gimmes in the early modern period, should be considered a mission as well - that is, not specifically granted by anything different from using movement (to look on your turn) or the patrol (to enhance sight on defense, at least spotting units you can't engage).
edit: You could also try penalizing ships by making them commit their whole turn's mission in one action. This in itself will make naval power as such build on itself with diminishing returns. (This works with keeping sight low.) Ships will slow down overall and 16 moves won't be felt as much in any but the extreme case of advantage. AFAIK this completely deposes the interface for Civ's units, though.
