Hi, I know how hard it is to get parts, I have been trying to do the same thing to my Camaro here in China.
Mine is a 2011 and I finally installed the LSD a few months ago. Because it was so hard to get parts, I found a used SS differential and modified the inner splines and CV joints of my stock 3.6 axles to fit the LSD. I didn't even need to change the driveshaft.
My parts list looked like this: SS LSD differential and modified axles... pretty easy and kept the cost down.
If you can find a 3.6 with a manual transmission, they should come with the LSD.
There are some people here in China that will modify the open differential to an LSD, but it costs about the same as a SS LSD and the options for further modification are limited. I'm not sure how easy it is to ship things between Russia and China, but I imagine its easier that US and China at this time...
Anyway, here is a video that highlights some of the procedure to change the differential, but doesn't go through the struggle of the all the mistakes I made along the way, ordering wrong parts and having stuff not fit.
https://youtu.be/pH0_IorWysE?si=l3odUC3Mjs6_Tbs9
Hope that can help you and good luck!