I would say that the difference is that ということで can carry a nuance of restating/rewording/clarifying/explaining something that the other two (which present the reason as a simple statement of fact) do not, and thus it feels most natural here, because the quoted line is expounding on the previous sentence.
I do not believe the other two would be ungrammatical, strictly speaking, though であることで would feel a bit stilted to me here. But I don't completely trust my non-native-speaker instincts on that last bit, so let's wait for Toritoribe-san to chime in.
Incidentally, variations like ～ということもあり（～ということもあって）would also be possible here, I would say.