Sounds to me like your water. Do you have trouble getting other kinds of beans soft? I have this problem when I cook in Vermont, because the water at my parents' house there comes from an artesian well and is very, very hard. You just have to cook it forever --- there's no real solution to that.
The thing about not adding salt early doesn't apply with split pea soup. If you're cooking beans and you salt the water (or use very hard water), there will be essentially no distinction between the beans being cooked and their starting to fall apart. If you don't want beans to fall apart, you've got to use softer water. But with split pea soup, you want them to fall apart, so it doesn't make any difference. Yes, it takes longer, but it doesn't really change anything else.
So, as others have said, just cook it longer. You can't really overcook split pea soup unless you burn it, so just add more water if it's getting too thick and keep cooking and cooking and cooking. You shouldn't need to puree it either: when it's done, it will thicken and the beans will fall apart to bits without any help other than stirring. That allows you to keep the ham bits off the bone, and the bacon, intact in the soup. I think split pea soup is a rustic sort of thing, and don't like it overly smooth --- but it should not be crunchy.