This problem has plagued my cocktail for years starting in about the early 90's. Before that, it wasn't an issue. From what I remember, it has something to do with the pectin levels of the Heinz products. You remember the old Heinz commercials with the Carly Simon Song, "Anticipation"? Well, pectin is one of the things that made it so thick. Tomatoes are naturally high in pectin but for whatever reason, their's is higher. It also appeared as if they changed the recipe somewhere in the late 80's and add in the multitude of ingredient combinations involved with Cocktail sauce......... someone once told me that's what caused the mix to turn gelatinous. To me, Heinz had the best flavor profile so I never monkeyed with substituting a house brand or Hunt's variety.
In bulk storage, we kept a wire whisk handy and just mixed it whenever we needed to retrieve some. We also used drip cuts for the portioning and these were held at room temp throughout the shift. They were also emptied after the shift and refilled as needed for service. There is enough vinegar and acid going on in the mix there's no worry for spoilage if you wanted o try this. The drip cut product was never mixed with fresh out of the cooler so, IMHPO, I can't see how a shift or two in a day would hurt it. However, I have no idea what new rules the inspectors might be enforcing given most places seem to refrigerate their ketchup.