If Edmure did use the Ford defence strategy you suggest and managed to bottle up the Lannisters, and thus stopping the riverlands from getting run through and wrecked, long enough for Robb to arrive with reinforcements and thus leaving the Lannisters stuck in the west, what is the Lannisters’ next moves? What does each of Tywin/Kevan/Jaime/Clegane, Tyrion/Clansmen, and Cersei/Joffrey do instead as their next move? Likewise, what does each of the other factions like Stannis, Renly, Varys, and Littlefinger do differently?

Well, I imagine Tywin, Kevan, Jaiime, and Tyrion would re-orientate their armies to get down the Gold Road to defend King’s Landing from both north and south.

As for the other factions, well, Renly might walk more gently with the Starks since they’d have more troops in the field/be less bogged down in their own lands. But otherwise I see stuff happening close to OTL – Stannis still needs Renly’s army, etc.