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.
Cinnamon adds a different spice profile than chili powder or red or cayenne pepper would. It is a common savory spice in Indian food and I believe it's also used in savory dishes in Chinese cooking. It's a very versatile spice :).
We also use cocoa powder in our chili as it provides a real depth of flavor (dark bitter flavors which are quite good in chili).
Both of these add some curiosity and difference to the chili without themselves adding sweetness. Usually they get added as a fairly safe way to add something "different" to standard chili.
Best Answer
The amount of grease the meat exudes is dependent upon the amount of fat in the beef. If your beef is lean (<10% fat), you will not likely notice a difference in the greasiness in the final product by not straining. If your meat is fatty (ground beef in the US can contain up to 30% fat), then the final product will have noticeable grease. The fat contributes in a good way (IMO) to the flavor and mouth-feel of chili if the meat is in the 15% range.