I knew a guy who once engineered a continuous yogurt-making machine… (maybe even the guy whose machine is in all the yogurt shops,) he was a engineer, not a biologist… but… you might be onto something.
There were some interesting aspects of engineering. Not nearly as many as he thought…
So. I tend to not use store bought sauces, can’t give advice on that.
But, if you haven’t considered it, you can reduce your overall work load by making sauces in bulk, and then freezing them. I got myself some giant icecube-molds to freeze into 1/2 cup blocks, and then transfer them to sealed vacuum bags.
Simply thaw and reheat for use. This also works quite well for stocks, or anything that takes hours of simmering.