My father brought us up on somewhat the same sauce except he used: 2 small cans of tomato sauce, 4 small cans of tomato paste and 4 paste cans water per can of paste, and you just skim the foam for a while in the beginning....I like to add a ton of basil because I like it sweeter and we both simmer it on low for 5 to 7 hours. We both now add about a tablespoon sugar after 3 hours and 1/4 to 1/3 cup wine (any but I like burgundy).
When they couldn't afford meat, they would simmer quartered cabbage (core holding it together) for a couple hours in the sauce which really mellowed it out and sometimes put hard boiled eggs and canned peas in it. We also boil browned meatballs or sausage in it the last 2 hours which makes them really tender. They also slightly brown a chuck roast and slide that in it for the last 3 hours and then cut up a bit and serve it instead of meatballs which is REALLY AWSOME!