So Darwin awards finalists are back with us again. Well...
both engines out for reasons unclear
Let me put it this way: CRJ is airplane. Airplanes are devices used to transport goods and people through air by method we'll call flying. To fly we need two forces: lift and thrust. Lift is provided when the device we'll call wing moves through the air. To propel wing we use thrust from engines. CRJ has it wings attached to bottom of the mid-fuselage and two turbofan engines attached to the rear of the a/c with T-tail above 'em. Now this configuration is susceptible to disturbance of air inflow to the engines if operated at high angle of attack. Not enough air to the engines means too much fuel (if fuel supply isn't immediately reduced) and internal engine temperature rising above the design limit temperature. Now this may lead to melting and welding of some engine components and if it happens engine can no longer produce thrust and it's not a good thing. No thrust soon turns into not enough lift and gravity takes over.
Before someone gets idea that T-tailed rear-engined jetplanes are dangerous by design, they're not! One just needs to keep his AoA low, as it's proved every day by thousands of CRJs, ERJs, DC9s, B727s, Tu134s, Tu154s, Gulfstreams, etc still flying happily around.
So how long can you stay at altitude in a glide?
Mind boggles on this one. If you're flying hi-perf sailplane in mountain vawe, as long as your oxy bottle lasts but if you're in transport category airplane, not even a split-second! Even if you go for your best glide speed you'll be plungin' earthwards with some rarely seen RoD - you'll get your 10:1 glide ratio but at quite high TAS. And if you go for windmilling restart of turbo-fan engine, you might need to pitch down in vicinity of 15° to get enough speed to windmill core shaft. This is a very scarry view, even in a sim.
About core lock: it happens on some turbofan engines in case of inflight flameout. Now the HP casing is cooled by stream of cold air going through bypass duct so it cools and shrinks more rapidly than core. Soon it contacts HP rotors and locks it until core gets cold enough and clearance between rotor and it's casing is restored. Was it relevant here: very small chance! Those GE's didn't just flameout, they failed after being severly overtemperatured, even partially melted!
failure to restart while relatively warm
I nominate expression "relatively warm" for "Understatement of the year award".
It's a shame such a beautiful plane was lost for no good reason. And too, too, too bad that pilots' families lost their loved ones. So next time when you ferry the bird or go up solo and have that itch to try something new, supress it. Thinking about the ones who will be hit hardest by your flight going awry might help.