As a battleship main in both World of Warships and Disco, I have personally adapted to the battleship changes rather quickly. (I understand that others have not.) Although the class is not perfect, overall I have to admit I enjoy flying my Overlord just as much now as I did pre-patch. The differences admittedly are night and day, in fact, my own tactics for fighting effectively on a battleship are considerably different now than pre-patch.
In my humble opinion, the direction being taken on battleships is the correct one, albeit not yet perfect. To bring them closer to perfection I would suggest two very basic things that will not only bring balance but will go a long way for people hesitant or unwilling to re-learn the class currently.
1.) Increase hull hitpoints on battleships to account for the slower movement / nerf to evasive actions one can take. As slow as they are, they should have a more tanky hull. Shields feel good currently, it's just the lack of hull capacity compared to the reworked battlecruisers that is nonsensical and feels bad for the user.
2.) Give battleship cores a buff to their overall capacity so they can deal with the drain a little better. Doesnt have to be anything insane, just enough that it's felt and meaningful.
Doesn't seem like much, but in my humble opinion will help make up for what others are seeing as "bad" changes. And from the pov of someone who is enjoying battleships right now, it will help balance the class where it needs help.
About the strafing/movement complaints, endless strafing on caps pre-patch was fun for some, but tbh is just cheesy garbage for most to deal with. That being said, strafing isn't gone, you will just have to use it thoughtfully and not in a brain-dead way. As far as the movement in general, you will need to think more about positioning when docking for example.