Dried Kidney beans for Chili

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.

• To try to engineer a Russian chili I would expect more indigenous foods.

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.

• The romantic version of the American myth about chili (in particular, Texas Red chili) frequently revolves around Cowboys planting peppers and onions on their most traveled roads. They would be carrying dried meats and, at night under starry skies, use kettles to cook the stew that became known as chili.
• What kind of story of Russian kindred spirit do you want to weave with your chili?

In fact, although the risk is low, the Penn State Extension does recommend soaking in the refrigerator, or using the quick soak method as opposed to an overnight room temperature soak:

To be on the safe side, it would be advisable to use the quick soak method: Bring water and beans to a boil, cover and boil for 2 minutes. Remove from heat and let stand 1 hour. Drain and further cook.

Similarly, the US Dry Bean Council recommends (emphasis added):

A 12-hour soak in cold water before cooking helps hydrate the beans and considerably shortens cooking time. Ideally, beans should be put to soak the night before they are to be prepared and be kept in a cool place, or in the refrigerator, to avoid any fermentation taking place. Before soaking, wash them several times in cold water and remove any damaged or split beans. Discard any particles floating in the soaking water, such as small insects from the harvest, specks of dirt or other contaminants.