I have long said that a PvE server would not be a bad idea for many reasons. And I still maintain that SoT can survive having a PvE server. However, I just don't know how you would be able to create it. So many mechanics that are for both PvE and PvP. Gun Powder barrels being one of them. Or how do you stop someone from boarding your ship and grabbing your loot if you can't counter attack? Honestly, I just think it would take far too much work on Rare's part to create a PvE server, which is why you won't see it.
That being said, I understand your pain. It is not fun when you just want to enjoy the beauty behind this amazing game. The swash buckling pirate experience is amazing. I guess if I am you, take some of the above comments and spin them into motivation to make some changes.
The first thing I would say is, keep an eye on that horizon. If I am sailing solo, I am not just looking for other ships, I am looking for mermaids and row boats. If I am at an island doing a quest, and it is taking a little longer than normal, I go back to my ship and double check, or I run the island and check all directions for any unwanted guests. If I do have a ship nearby, then I am watching them even more, especially looking out for any thing between me and them that might indicate a swimmer or rowboat coming towards me.
Sell often if you don't want to lose the loot. It is not always convenient, but selling often at least ensures you get something for your efforts rather than nothing at all.
And try and enjoy the experience. Don't get to rattled by the fact that even with doing everything you can to try and avoid bad situations, they can and will happen on occasion. If you do become more vigilant, those bad situations will be a lot less than if you are not vigilant. But they still will happen. And it might not even be another player. You could get the kracken, meg and skelly ship, while a storm rages above, event that always is a blast on a sloop solo.
For me, the biggest thing I had to learn was, when I play the game, it is about the experience, not the loot. If I lose, I try to learn from it and move on, but I don't allow myself to get upset. The only time I might get upset is if the encounter is toxic. But having a pirate simply take your loot is not toxic. And for all you know, they may have had a quest on the island you were at, and simply wanted to force you away from the island.
So, keep your chin up, enjoy the game as it is, even those bad situations.
Fair winds and calms seas to ye matey.