I really, really don't like the "alien weapon is destroyed on death" mechanics. Sorry for the harsh words, but to tell you the truth it feels extremely unconvincing, forced and gamey. A pistol is a goddamn pistol, it can't just spontaneously burst into flames like a letter from a spy comedy show. And even if it could, enough would remain to investigate it anyway (especially if we had many of them).
However, I really like everything else in this thread. Despite some initial reservations, I like the "psionic trigger" idea, the "research alien corpse to enable Alien Containment" idea and so on. I'm only worried that the game might become too hard at some point - perhaps the aliens' progress could be slowed somewhat to accommodate for much slower research? Or maybe it wouldn't be as necessary?