There is nothing there that stands out as a cause for your problem. I have had Tomato sauce separate depending on the brand of Tomato Paste used as some are more coarse than others. You may try letting it cool and running it through a Blender or use a Submersion Blender to make sure the the ingredients are broken down very fine. Another option is to reduce the Vinegar by 1 Cup and add 1 Cup of Mustard. In that large a batch it should not be real noticeable but Mustard has some great Emulsifying properties that will help bind the sauce. While Ketchup is an option, it will require a lot of experimentation as you will be replacing all or most of the Water, the Tomato Paste, a portion of the Vinegar and some of the Corn Syrup as all of these will already be in the Ketchup. At least a short cook time, heating to a simmer, is needed to help meld the ingredient flavors and add to the shelf life by killing any Bacteria that may be introduced from the ingredients, pot and mixing utensils, and from contact with the air that is incorporated during measuring and mixing...JJ
