Thank you for your response. I would only add that Zakaev (whom I admire a lot) himself stated that "Chechen Islamism" is Lubyanka plot to destroy the Chechen resistance and to split the Chechen society. Of course the resistance had to turn to some Islamic identity but to call them "Islamofascists" is, on my opinion, a big exaggeration and misunderstanding that even undeliberately plays to benefit the Russian-Kadyrov regime. I wouldn't support such kind of propaganda. Also, Andrei Babitsky himself had been in Afghanistan to investigate "Chechen ghost" stories and did not find a tiny evidence that support such claims.
Well, I for my part would only add that if the [North Caucasus] Islamic resistance wants to avoid the Islamofascist label, its members need to stop writing and behaving like Islamofascists. Many of the statements that are published on their websites are outrageous, and could be classified as hate crime.
On the other hand, I'm sure that very many of the stories about Chechens in Afghanistan, Pakistan and elsewhere are untrue, and are engineered for Moscow's propaganda purposes. My suggestion - and I believe it's a moderate and reasonable one - is simply that these stories need to be looked into and analysed, and the results made publicly available.