how to cook nondescript venison in a cast iron pot so its tender?

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.

A third option is to mince it and bake something like a venison cottage pie (you've ruled out burgers). This will have the effect of mechanically tenderising it as well as breaking it up into little pieces which won't seem as chewy. You may want to mix in a little beef mince (of the fatty kind) if you suspect the meat is rather lean (and tough venison can be). Of course, you need a mincer to do this.

For getting tender meat, you typically have two choices --

1. Low and slow cooking

2. Hot and fast cooking (ie, a quick sear, left rare or medium rare)

Option 1 is best when there's lots of fat, which is rarely the case in game meat.

Option 2 is a problem for unknown game meat, as without knowing what animal it is, we don't know what the risk of parasites are. (so it's important to know what you're buying).

If I had the meat, I'd probably be inclined to use mechanical tenderization (ie, pounding or stabbing) if you want something more steak-like, but cook it to medium, or a low and slow cook but be mindful of how you cut it up. You could even cut it up for a stir-fry.

As you've then given us the restriction of only one choice of cooking vessel, I'd say you're best off with the slow cook. I'd personally go for stew or pot roast as the slow wet cooking tends to yield tender meat even if it's not all that fatty ... but you also said 'minimum amount of extra ingredients' ... and that starts getting into 'recipe request', which the folks on this site tend to shut down.

I would be personally inclined to make a brine and make a wilder version of corned beef. I have made something similar with the tougher parts of beef ie brisket.

The process of osmosis hydrates the muscle tissue, allowing the cells to hold on to more moisture while cooking. This may give you the chance to do a slow-and-low cook.