[b]The River:[/b]

It doesn't seem to be too far off canon but how we handle it will be, no worries there I think.

So we're fine with starting as described, and then how far ought we skip, you think?

[b]Clash of Kings:[/b]

Yeah, true. Tyrion and Cat will be busy half the time with travel and misunderstanding. Cat would still want to head to King's Landing to tell Ned about the attack, though we could have her not have bothered with going to her sister. We could just have her take Tyrion to King's Landing and have him sorted there? It would change things, she would be around to help her husband but then she could let Tyrion go in a sort of exchange. Yes, Joffrey would want his uncle freed but if we let Cat try to reason before acting out, we could have the exchange done in secret while Robb (not knowing about a secret truce of sorts?) could still start a war, since everyone (save for Joffrey and Cat) know that Ned is safe?

I know she loves her children but they would be safer with Ned alive, rather than Ned dying. And if we have Ned talk to Joffrey in private, rather in public, he could get more leeway. 

Then Petyr could be under the impression that he can still "save the day" while also keeping his pawns in check?

We could have Joffrey and co. smuggled out during Blackwater? You said you wanted him to be with Tyrion, we could do that, Petyr could use the chaos to sneak him and Arya? Not sure if Cersei is invited or not. And then there's The Hound as well.