"It's not as if chants of "Death to Russia" are common in Iran. Why should Russian officials care about an Iranian N-bomb..."
Of course they don't, we are Iran's primary enemy and it serves Russia strategic best interests to see our nation go to crap when NYC or LA gets vaporized. What I would suggest is that the USA provide Chechnya 'peaceful' nuclear technology, with our FIRM guarantees that we will monitor the situation to make sure all the fissal material gets back to us. It's what Kennedy or Reagan would do in dealing with the Russians. They only respect and respond to hard ball.
Islamists in Chechnya and bin Laden are the best friends. As well you can give nukes directly to him, "with our FIRM guarantees" of course. A jolly good idea!