We've been to the russian side (Bezengi) in july, bagging the easier 4k peaks. See report (in german).
As I got it, access to the ultimate border zone formally is "forbidden", beginning with the upper bezengi glacier. I.e. all the people starting to shkhara, katyn, jangi from the russian side do that illegal *g*.
Apart from that you just have to tell your plans the rescue station at bezengi base camp; the only further red tape is the border zone permit, which usually is provided by base camp -- just mail/call them in advance.
Martin