Wait nevermind DNA yes we do.

Yeah, the whole thing is they find out his DNA matches a Synth which ran away. He's not a clone.

So Danse joined the Railroad, got his memory erased, relocated to Rivet City, and joined the BoS.

We don't know that he joined the Railroad. The institute seems to think he suffered brain damage if another thread is to be believed.

It's not clear when Danse was replaced, but it make more sense to replace someone, who is already a BoS knight, then someone who is not.