I think at the moment, Chechnya is OK. Of the 3 dodgy areas in the Caucasus, Ingushetia, Chechnya and Dagestan, I would be comfortable to go to Chechnya right now, but probably not the other two.
They have been doing all sorts of big international stuff in Chechnya so far this year. There was a big well publicised football match with loads of Brazilian internationals. Ruud Gullit, former world and european footballer of the year arrived there in February to take of the Chechen football team.
Keep your eyes on it, as things can change fast, and of course security in that region can never be taken for granted, but I think its maybe the best chance to visit Chechnya since 1991 right now. Grozny has been rebuilt in a pretty grand style from what I have heard from locals and would definately be interesting to see that.
Also looking at your map .... you can drop down through the Nogai Steppe from Yuzhno Sukhokumsk on your red line, south to Terekli Mekteb ... which is in the Nogai region of Dagestan. Thats an interesting part of the world and the Nogai people were very warming to me 2 years ago. So warm that I struggled to get away. It was endless hospitality.
But if it were me, I would probably avoid Makhachkala and Khasavyurt at this present time.