Clandestino ... "Come to conclusion that either manufacturer lied to you or you don't know the whole story and start descending"
Think about the circumstances of their arrival at FL410. Aircraft have recommended climb profiles for a reason and, should you choose not to follow them, you do so at your own peril. If you get well behind the power curve at the edge of your aircraft's operating envelope you should choose to descend of your own volition. Either way it is soon not going to be an option. CRJs fly quite well at FL410 if you abide by the performance tables and recommended climb procedures. It is not dangerous or even risky but it is certainly no place for amateurs or cowboys. As for the relight procedures ... follow the AFM. It is no time to start being creative.