One thing I did notice in your reply here. You "mix the fat and the meat.
First suggestion. If you've getting an overly fatty taste, AFTER cooking, try to get rid of as much fat as possible. Don't mix it in.
I think if you continue to cook it, the fat won't render more, but the meat will dry out.
There's a bunch of post on the internet that I've seen that talk about how the fat breaks down, but cooking longer won't make it break down more.
The breakdown of the Collagen, it's called.
Have you done a brisket? Here's a tip. When it's cooked and before slicing, take a knife and scrape off all the fat. When it's cooked right the fat will literally scrap off very easily.
Does that help?
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Smokin Okie
It's done when it's done
Cookshack BBQ Guide Page