Pretty much an accurate description. I had gone through russia on the similar trajectory twice this year and helped a friend to get 3 year multi-entry visa in Tbilisi, Georgia. No issues applying for a visa in a country different from citizenship.
It is very difficult to get olde good transit visa, but multi-entry tourist visa? No problem. Just have a tour agency (which in Tbilisi is located in the same building as consullate), fill out paperwork with route, hotel reservations and mandatory 90-day russian health insurance purchase.
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