Andrei, your otherwise awesome writing really drops off the closer you get to hard science. This article is no exception. The stratosphere is a specific height above the earth. Nothing in this story, in the historical record, or in NASA's acknowledgement of the action, provides ANY suggestion that he made it to this altitude.
Moreover, as described there are many things about the story to suggest he did not.
If your title had been: First man to attempt to blast himself into space. THAT would be accurate.