I mentioned this in another thread, but it doesn't really make sense that Jason came to help against Terminus. He wasn't a big threat like the Talons were, and how did Jason even know to come? Plus, I'm pretty sure he's in space with Kori isn't he?
That's not the sound of heads exploding, it's the sound of people putting their wallets away. If you want to alter Tim's Robin continuity, I think it would be better to say that Bruce had previously tried to make sure people couldn't tell when there was a new Robin (Dick and Jason had worn the same costume, go with the old "Jason dyed his red hair black" thing) to ensure that "Batman and Robin can never die" kinda mindset in criminals. To that end, when Tim debuted wearing his all red costume, TIM thought of himself as "Robin" but other people (heroes, villains, the media, whatever) referred to him as "the new, RED Robin" and that THAT is the origin of the name. Because otherwise it's a kinda stupid, non-threatening name, and there's already a precedence of heroes with the name Robin.
This makes a lot of sense. He's still Robin, but wants to be a little original so gets a new suit. The rest of the world still recognises him as Robin but sees he's different to the previous two - although everyone would think there was only one - so they call him Red.
I know they died but maybe in a flashback or something? Or we all know that in comics being dead means next to nothing. Maybe they could be cloned and used against another kid team like the Titans. I just think the Harm Armory was a cool idea they left under developed.