I like both PvE and PvP, but favor PvP because it's more dynamic to combat with other pirates and it feels much more rewarding when winning against them. I strongly believe SoT without being PvEvP wouldn't work. But as a long time player that started playing before release with 100% reaper unlocked and 100M+ gold earned the game is becoming stale. Most ships me and my crew finds are newer players that doesn't put up much of a fight, if at all, usually with low amounts of loot, and we don't really need the gold anyway. I still enjoy the game, but there's not much challenge or incentive anymore, and even thou I do try to slowly work on some of those more grindy commendations it lacks excitement.
There's been some suggestions for ship more ship customization, imagine if that was unlocked from leveling up your ship! Preferably it should be something that stands out and not just a different cosmetic like the once we have now (hull, sail etc). Maybe a different rig or sail type that can be seen at a distance, naming your ship, custom stuff in captains cabin or other places around the ship, or other suggestions that I'm sure others have had before. The main thing thou is that once your ship sinks, you lose all progression and some of it is rewarded to the ship that sank you, probably dropping similar to emissary flags (marked by birds and floating for a fair amount of time in case of multiple ships fighting). That means you need to be more careful with your ship, and it also means that when you see a ship with these customizations you know it's a crew that has been able to keep it afloat for a long time, so flex those customizations with pride!
Leveling probably should be part of the normal game loop, so you get XP while doing the normal stuff for the normal factions, to make it available for everyone, but you should get a big amount of XP from sinking other ships with high level, to encourage PvP and also so you get a nice reward even if they don't have any loot. This means more risk hunting other ships, making only the bravest pirates dare to risk it, but the rewards are exiting for the ones that do!
There are some details regarding crews that needs to be worked out. I'm thinking the ship should belong to the person starting the session, and you probably shouldn't be able to transfer XP to another crewmembers ship to avoid just using low level ships when hunting others. It should also be optional if you bring your custom ship, or just a normal one that cannot be leveled, since you might not want to bring it if you're playing with random people etc. Maybe a separate option if you go solo, so you can level up as a solo, but since it's hard to solo not lose your crew based ship. Perhaps also it's separate for different ship types like sloop, brig and galleon. Things like what happens if the person who started the crew leaves the session needs to be worked out. You don't want to lose your ship when you can't defend it, but it's also not good if you can just ditch if things look bad and save your ship like that. Maybe it needs to work similar to emissary flags that you can remove it at outposts, but of course if the server crashes or something you shouldn't lose it. Perhaps it takes a bit longer to remove then the emissary flags, so you can't just ram an outpost and rush to lower it like with emissary flags.
It could also be that it's just cosmetic, but one option is that it goes beyond and add RPG like customizations where you can change your ship to fit your playstyle. Not going into this in detail, since it's a big topic on it's own and probably also suggested earlier. It could be things like fewer cannons for increased speed, or a front facing cannon but less speed, or more sails, but that require more effort from the crew to operate so the ship ends up slower/less maneuverable unless the crew can keep up. This is of course something that would need to be carefully balanced, and one reason it might ok to have something like this in this context is because you can also lose it so it doesn't just become a new meta where everyone end up with the same style ship anyway. Also if it's balanced properly what's best depends on your style and what you're doing. One option is also that the first few customizations you can unlock for your ship are purely for fun, but once you progress pretty far on leveling you can get things that actually change how your ship behaves. Maybe the final level is an option to unlock a man-o-war that can take 6 players, and of course if you sink you lose it and have to start over from 0 XP.