How to 'stretch' tomato ketchup?

I think your answer is found by responding to the question: "Why do I make my own ketchup?" Heinz ketchup is delicious. It is also produced in mass quantities. You'll never compete on cost because of economies of scale. If you are purchasing ingredients, homemade ketchup is just going to cost more. This brings me to the question I posed. If your answers are "it's fun"...."I like the flavor"...."I prefer my ketchup over Heinz"...anything along those lines, you may just have to accept that yours will cost more to produce. Maybe find a way to buy tomatoes in bulk? You might get even closer if you grow your own tomatoes. Even then, the cost would likely be more when you take all of the production variables into account. Any "stretching" will change your recipe, probably at more cost, possibly at risk to the flavor you have developed. If you are trying to make ketchup to save money, there are probably more impactful home financial strategies you could employ.

Honestly, if you want good homemade ketchup you don't stretch it, if you dilute it or cut in lower quality ingredients the result won't be as good. However, $4.50 is a lot for a can of tomatoes, my suggestion is to use tomato paste and add water rather than use canned tomatoes. Tomato paste is not as good a flavor as canned tomatoes but it is far cheaper, and all the major brands use it as a base. A thickener/stabilizer will help to keep the mix integrated.

I've never made it myself but here's a recipe for ketchup using all paste. You could try a 50/50 mix of fresh to paste and see if that makes a good balance between price and flavor.

One thing I wouldn't use is corn syrup, it isn't going to help thicken anything any more than sugar and it doesn't add any character.

I guess comments are discouraged as answers, so I've moved this to an answer.

You could stretch it with Heinz (or other brand, French's maybe) ketchup. If its a taste thing, it would lower the quality but still be better than store bought. Since you're looking to lower sugar/corn syrup content, try reducing the sugar in your recipe to compensate for the extra sugar in the commercial products. You could even remove it entirely and adjust upward from there.

Alternatively you could try beef or chicken stock, heavily reduced, but this would cause significant changes to the taste and you may still need to adjust the water content and add a thickening agent. If you are making your own stock, pork bones can often be found for an exceptionally low price.

You could also try similar vegetables that are cheaper than tomatoes. Throwing in a few onions could stretch it a bit farther. Hot peppers could add some spice and make it go a bit further as well.

That also sounds very expensive for canned tomatoes. I've gotten them on sale for 28 oz for $1-$2 CAD in the past (this depends on your location, of course). Consider shopping around if you haven't, or switch to a cheaper brand (you can doba taste comparison to see if the quality is similar). Amazon currently has canned tomatoes for $0.13 USD/oz, so consider an online source as well. Otherwise you can probably can your own tomatoes when they are in season for cheaper.

Not directly part of the answer, but I also found this article from the Washington Post that might provide some insight:

Americans didn't always have a singular idea of what ketchup should taste like. Indeed, the first ketchups weren't made from tomatoes at all. According to "Pure Ketchup," Andrew F. Smith's definitive history of the condiment, the first known English-language recipe was published in the 1727 edition of E. Smith's "Compleat Housewife" and called for anchovies, shallots, white wine vinegar and spices such as mace, ginger, cloves and lemon peel, making it closer to an Asian fish sauce. By the early 19th century, cookbooks offered a range of recipes for ketchup made with walnuts, mushrooms, lemons, cucumbers, oysters and, of course, tomatoes.

and

Heinz's recipe is a trade secret. But some of the brand's earliest recipes are not. Its first blend included cloves, cayenne pepper, mace, cinnamon and allspice. The second had black and white pepper, ginger, mustard seed, horseradish, celery seed and brown sugar. Vinegar and salt were added to taste.

You could consider adding more ingredients to boost the flavor, and then water and a some amount thickener to stretch the amount of final product.