it turns out tough and dry when I tried to braise it, and the longer I cooked the tougher it was
Then it is impossible to achieve what you want.
All "low and slow" methods overcook the muscle tissue, making it tough. At the same time, they melt the collagen in the meat, turning it into lubricating gelatine. The cooked meat then consists of muscle fibres embedded in the melted collagen, and is fall-apart-tender. You have probably had it as pulled pork or similar dishes. The requirement for this type of cooking: you need a high amount of collagen. If you don't, you will just end with the tough muscle fibres sticking to each other instead of swimming in collagen, so it will be one piece of tough meat.
How do you know that a piece of meat has enough collagen? You can use heuristics such as taking a look at it and recognizing the amount of connective tissue present, and also your knowledge about the animal and its parts (older animals and more supportive parts have more collagen). But the final test is cooking. If the longer you cook, the more tender the meat, it has enough collagen for low-and-slow. If it turns tougher, then it is not suitable for slow cooking.
The second option is hot-and-fast. It always produces AGEs. You excluded this.
The third option would be sous vide. As you 1) specified a cast iron pot, and 2) probably don't have a sous vide stick to suspend in that pot, and 3) don't know enough about the meat to look up the proper time and temperature even if you have the stick, that seems also out of question.
It seems that you need to buy some other meat. From there on, the proper procedure is to follow any recipe for low and slow cooking you choose.