What's the source of the sweetness in tomato sauce that's simmered for at least four hours?
I think caramelization might be the wrong word there. I would go for concentration. While some caramelization does occur around the rim of a pot of tomato sauce as the sauce reduces (and it's good to stir this residue into your sauce), the main increase in sweetness is due to a concentration of all things tomato-y as the water in the sauce evaporates.

Speeding up this process is not only possible, but, in my opinion, highly desirable. A long- simmered tomato sauce can often have an overcooked taste to it. One method to speed things up is to strain your canned tomatoes through a fine-mesh strainer, or something equivalent. Use what remains to start your sauce in the normal way and keep it at a simmer. The liquid, however, you can heat more rapidly at a low boil since there are very little tomato solids left in it to get that overcooked flavor. Once your liquid has been reduced by 60-75%, you can add this back to your simmering tomatoes.

If you start your sauce with fresh tomatoes, the quickest way to accomplish this is to freeze them. Once thawed, all their liquid will pour off easily. Boil down this liquid as described, quickly sauté your remaining solids, and then blend them into your reduced liquid with an immersion blender. This results in a very rich and flavorful thickened sauce that still has the brightness of fresh tomatoes and can be done in a fraction of the time mentioned in your question.