Yay, this idea has merit. Jason's scowling face is in the dictionary under the word "outsider", and he's desperate for a sense of belonging.
I also want to give Cass something to do, and since she's already been there... I could see Jason approaching Cass out of respect, and Cass wanting to rejoin the Outsiders to be back in action while being away from Gotham for a while. He admires her fighting, she appreciates his way with words (she likes snarky people). Until she can be Batgirl again, let's have her take the name "Blackbird", the code name that Babs used for Bruce when he went down in Hush -- a way for Cass to say "I'm Batgirl" at the same time she's putting distance between herself and Bat memories. Cass instantly carries out Jason's orders most of the time, but it's not infrequently that she says "no" (and she doesn't say any more than just "no"). Being bluntly contradicted enrages him at first, but of course it turns out she's always right because of her incredible perceptiveness. It eventually helps him (it deserves to be said again) "level out and realign with the white hats". I can also see Jason getting Neapolitan ice cream from refrigerator when Cass walks in to the kitchen for some orange juice.