First I want to say I love certain aspects of this game, and completely despise others. There has been many many requests for a PvE servers and the general response from many players has been a loud NO. There are some good reasons for this as the core gameplay relies on player uncertainty to create the high moments of the game.
We still have a problem though, people looking for action on the high seas feel like they have been left high and dry... between unequal servers, abundance of sloops, alliances, and overwhelming feeling of PvP is partially "griefing" due to poor design. So instead of a PvE server, I propose a PvP server for me and my blood thirsty brothers to have a place to play.
Server wide voyages, with loot value upfront
I'm not to particular on how the details of this is implemented. But making it so another crew and I could potentially have the same objectives increases the probability of running into each other naturally. Loot can now be contested before you dig it up. Its no longer your voyage as its available to everyone. This also means you can predict where people might be. And there is still some room for avoiding people if you just want to go after lower value loot, or something that isn't contested.
Limit the amount of loot per voyage / health of skeletons
No more 6 hour athenas, we want to keep the amount of time investment on an island minimal so people are nimble and not tied to an island for long stretches of time. They should be quick and easy instead of a slog, so you have time to fight other players.
Actually no more athenas
Athenas are rubbish, they are just time sinks.
Limit ship types
No sloops vs galleons make a small PvP class, and a Big PvP class. Either sloops+brig and brig+galleon or just brig servers and gal servers. Make teamwork an important aspect of this mode.
No alliances/merchants...
... Do I really need to explain this...
No meg/kraken/skellys ships/fort
Design a fort like event initiated by players and creates a PvP flash point. Forts were glorious but the idea behind. Being initiated by players is to give a player that is already on the server an advantage over fort hoppers. If you want those big epic fights you can just re initiate it over and over and over again instead of jumping from server to server to server.
Although I'm not to particular about keeping meg/kraken out. If done right players will be fighting all day and they'll never worry about the lack of "content". They could add some options in like enable/disable kraken/meg/ccbs/controller only etc...
Increase player count, or decrease map size
Shouldn't be hard to run into others... like it is now. I wouldn't mind if the running into other players was actually 15/20 mins... it sometimes feels closer to 2-3 hours.
Separate reputation and a new ranking system
Obviously people on the "PvE" servers should have a different progression + ranking for matching players up appropriately. One could argue that there should be some ranking system already in place... since that is an important part of any game that has PvP to any extent...
Nothing has come close to the pure joy that is fighting other players in this game. I want to keep that aspect of the game that world PvP creates. Its the funnest messes I've ever been apart of since golden eye. I think for people that enjoy action this game just doesn't do enough to curate those moments. There is a lot of wiggle room in the idea. You could make it round based with 3 maps already on the wheel and just let a bunch of players fight over 3 chests... or not, just introduce new jobs on a bulletin board as players are playing. They can play with the numbers a bit, force players into bottlenecks or just throw lots of voyages at players leaving room to be non confrontational.
If they wanted to be overachievers.. you could have even more fun with this, everyone is in a solo instance until they pick up a voyage, its effectively like round based matches but hidden. You grab a voyage that other players have already put down and dynamically join their server. Its kind of like this rumor I read about for star citizen, about 76 years ago when the game was announced, where you'd dynamically be matched while in hyperspace drop out and have a PvP battle. But this would be making it explicitly a fight over every piece of loot.
Obviously depending on the details could make it purely confrontational, to something similar to what we have now with higher chances of running into players. Rare needs to find a way to bring PvP into focus without it being detrimental to the more friendly player base. They need to do it before us PvPers are gone. They are in luck! There is nothing on the horizon that is tickling my fancy, so they have more time then deserved. But I definitely won't be able to endure the slog of a game forever because the fun aspects of it have become significantly harder to find as time goes on.