If you're unthawing them in your refrigerator (below 40 F), then you should be just fine. Most beasties don't reproduce at any significant rate below 40 F.
There isn't a clean cut off point because it depends entirely on the existing level of contamination present in your meat.
You should be aware that repeated cycles of thaw/freeze will really damage the texture of your meat. The cells simply do not hold up to that.
I think you've got a wide berth of possibilities but what's above seems pretty restricted. What you are listing above sounds like a pretty straight-forward Midwestern American chili. It has the features of the standard chili spices, beans and tomatoes, with a nice variety of meats.
As @Cold suggests, beets would be great to add for their sugar content. However, there are quite a few American recipes that utilize potatoes, so you might seek those out. Are there other vegetables to substitute that you recall as more native? Other beans maybe? How about caraway, dill, chervil, tarragon?
Vodka would seem like an easy route to go to appease the indigenous aspect, but I don't think it would yield much results in terms of impacting the flavor; especially in the context of the extant chili recipe. Unfortunately, I can't see the benefit of buffeting vodka against the flavors of cumin, coriander, clove, let alone hot peppers. On the other hand, Russians produce some amazing beers (I am a big fan of Baltika), and I would recommend looking into switching to a lager flavor or Imperial Stout as I mentioned above.
But for real, my spin would be to approach this from a Solyanka point of view (which would definitely give you ceiling room to try incorporating Medovukha); or really any of the other amazing cold Russian soups. Or perhaps try to incorporate mini dumplings like Pelmani, mini Kotlety, or use Shashlyk-style prepared meats for the chili. I would also consider trying to get some lamb in the recipe, in particular at the expense of the chicken.
But don't forget, chili is all about what you want to put into it (<-- self-promotional plug); not what the standard template lists.
Best Answer
The photo on the left, specifically the upper left quadrant appears to have a concave shape that would make one think (at first glance) of the short ribs, but the ball joint and size definitely is the give away here. Assuming the dish it rests in is an 9x13 casserole dish you are right that this is probably from a lamb rather than a beef. But the folks at Victorian Farmstead provide a photo that makes it completely clear that we are indeed looking at a "Bone In Leg of Lamb"