Are there interior guided tours of the Seven Sisters?
Upvote:2
You may have some luck with the Moscow State University building:
It has a museum (I think this is the one). Unfortunately it's not open to individual visitors (except for MSU students / staff), but it is open to organized tours, and it's located pretty high up in the MSU building. You may be able to find a tour company that can organize a tour here (or if you're willing to go through the bureaucracy you can organize one yourself).
From what I saw (admittedly many years ago), if you look like a student and enter the building through one of the auxiliary/side entrances, chances are nobody will check your student ID and you will be able to get in. However, security may be tighter now.
Being an active university, I wouldn't be surprised if MSU hosts some events/lectures open to the public, which may offer a legitimate way to get into the building. I don't know any specifics though.