I'll go a two options route as well. In both options, Morrison's story ends in the old continuity.
Option 1: Batman first appeared 6 years ago and operated as an urban legend for roughly one year before the formation of the Justice League 5 years ago. Only active Batfamily vigilantes are Dick as Robin and Babs as Batgirl. Both would be either late teens or early twenties. We'd get roughly a year with Dick as Robin before he moves onto Nightwing. Killing joke happened or didn't happen as preferred.
Option 2: Batman started his crusade 10 years ago, operating as an urban legend for roughly 5 years until the formation of the Justice League.
Year 1: Batman begins his crusade at 22 years of age.
Year 2: Batman brings in a 14 year old, newly orphaned Dick Grayson.
Year 3: Babs begins operating as Batgirl (age 16).
Year 4
Year 5:
Year 6: Justice League forms. Dick goes to college. He leaves the Robin mantle to Jason when he takes up the mantle of Nightwing with some incarnation of the Titans.
Year 7: The Dark Year (Both Killing Joke and Death in the Family occur). Tim becomes Robin in the aftermath
Year 8: Bruce meets Damian. Under the Hood (Jason returns like in the animated movie, does not become the antihero we know in RHatO until the start of the n52.)
Year 9: Combination of Batman R.I.P. and Knightfall. Bruce "dies," and Dick takes over as Batman with Damian Robin
Year 10: Bruce returns.
This way, Dick has 4 years as Robin, Babs has 2-3 as Batgirl pre-paralyzation, Jason is something of a short-lived Robin, and Tim gets about two years as well. Cass and steph could have their origins around the time of Tim's tenure as Robin.
In either case, I'd have Huntress (Bertinelli) in Dick's orbit. She would be a strong character in her own right, but they make for nice foils; one primarily wants to punish the guilty (and protects the innocent as a function of that) while the other primarily wants to defend the innocent (and punishes the guilty as a function of that).