So get Kurn to join like Alexander did.
That might not have been as easy as it seems. Martok asked Worf to join his house because Worf saved him on more than one occaision. And when he asked him, he thought Worf was alone, he didn't even know about Alexander. Asking Worf to join his house does not automatically mean everyone related to him gets to join. It's like if you invite a friend to come over and they show up with a bunch of other people you didn't even know about.
Given the cop out ending we got, I always had the feeling that Kurn was intended to return at some point. Given the war and all the Klingons at the station its surprising they never had a chance encounter between brothers.
I felt the same way. I just knew
we'd see Kurn again and this would ge "fixed" somehow. Klingons are supposed to have super strong, redundant physiologies that heal quickly so what's to say that Bashir's mind wipe would actually stick, you know?