Sugar is considered a liquid when cooking and with increased temp you'll see a decrease in density causing the liquid to become less viscous. There are many other ways to make your sauce thicker. You could obviously use different thickening agents like flour or cornstarch. You could reduce it down further in the process of making it. You could use thicker ingredients like tomato sauce in the making (that's if you are using tomato sauce).
As to the burnt, sugar will always caramelize, its why we use it. It encapsulates the meat, gives a bit of flavor, and holds in the moisture. That being realized, burnt is not good. That is why for the most part normally sauces , mops, spritzes, are saved for the last hour of cooking. That's is usually the lowest and slowest heat. If you start saucing immediately after putting the meat on the pit, it probably going to burn every time.
Sounds like maybe both your problems would be helped by one change, reducing the sugar (Molasses), content in your sauce if possible.
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Hope it helps, if you'll allow us to see your sauce recipes I am sure we could better help you.