My split pea soup has nothing in it but split peas and ham with a little sea salt added. I love it this way but but will try adding some of these other things that sound so good.
A consideration is always modifying the canned soup. My mom called it "kinda home made" when I was growing up. Ex, we would buy a name brand spaghetti sauce, but then put all sorts of mushrooms and ground venison and stuff in it. So I'm thinking you could do the same thing with the pea soup, so that you don't need to cook the peas, etc if you're feeling lazy/rushed. Just add the ham and carrots to that, and some spices to balance flavors.