I see what you mean, and I do agree that Babs should play a more active role since what Booster did affects her the most. The timing of it might be ill however since: a.) this arc screams that it's setting up something. Bruce was never able to have those inspiring talks with Booster so his replacement does. Perhaps a connection to lost in time Bruce? Maybe though if I recall the plans for including Booster fighting along Bruce during Final Crisis were changed so that could be the case later on if this was a set up.
b.) Damian is the son of Bruce and a future Batman. I half expected this arc to end with Rip visiting him. Tim might make sense but then again this is the really intense Tim that would likely demand that Booster save Bruce right now. Damian might not like Booster but he listened to Dick when he told him to back off.
c.) When Barbara finds out the arc should center around her and Booster (perhaps even the Joker) not Bruce being dead and how he differs from Dick.
BTW wasn't the cabins locked? I remember that Booster could only find them with the help of Skeets anyway. And not many people can even enter the caves without triggering some alarms. Booster has already been there at least 7 times. The point of the Jokers' behavior in the Killing Joke was to make Jim suffer the worst day of his life on a personal level. Flashing beat up pictures of Booster, a guy that at the time was a newbie in the league, doesn't have that personal touch. If Bruce was keeping this all a secret from Booster it might be likely that he hid it from others. Let's not forget Booster left blood at the bottom of the staircase.
I took it at them being ironic that their pretty much stuck in the same situation. Booster can't/won't risk the cliche "would you kill if you could" time travel question anymore than Dick will kill the Joker. Different environments same answer. I think this was meant to show how lighthearted Dick is compared to Bruce. With Bruce there was a smile but the cowl never came off. There was always a distance while Dick is the sort of guy Booster can get personal with.
Personally I didn't care one way or the other for the BB back ups until Black Beetle arrived. Just never clicked for me.
Graysons' at Christmas: Why is it awkward? Because their not at the circus? I find it believable that the Grayson would go somewhere more comfortable every other Christmas than deciding to work. Families take trips for the holidays. *Shrugs*