Hmm, what sort of actions would be allowed during the reaction phase? In your example about the party vs. ogres would the ogre's reactions have any effect on their defense? Say one of the ogres tries to block the fighter's slash at his leg my shifting his foot back or blocking the attack with his club, would that have an effect on wether or not the ogre was hit?
I really like your idea of Team 1 Action->Team 2 Reaction->Team 2 Action->Team 1 Reaction.
I think it would make it easy to understand what happens in combat if the the current 6 seconds it takes a character in pathfinder to take their turn was turned into the "Team 1 action -> Team 2 reaction" and spell effects and attacks were resolved at the end of that..err.."turn" lets call it. That way the enemies reaction could increase their defenses, OR ready for a large action they plan to do on their turn, leaving themselves open. Flatfooted opponents wouldn't be able to defend themselves and their defenses would suffer as a result.
At the end of the "turn" when attacks and spells are declared and after reactions are declared, they would happen in order that the actions were declared. So in your example, first the fighter's swing, then the wizard's spell, then the rogue's flank, then the cleric's spell.
What do you think? would the whole "reaction" thing be too much of a change to how pathfinder's defenses are calculated? Hmm, what would it be like if the party split their actions up into sections..Say, since the fighter would want to get the "flanking" bonus with the rogue the fighter says he waits to make his attack until the rogue is in place. Would he then be able to make the attack? I guess this is doable in current pathfinder by using readied actions..Hmm.
Now another note. What do you think would happen if in your example, with the rules I suggested, would happen to a character's actions if the target of their action has changed since they decided on what they were doing. Say, the fighter slices the troll's foot off, the wizard casts grease, and the troll falls down to the side where he's missing a foot. Now the Rogue can no longer get behind the troll because now he would have to run around the troll, and that's farther than he can move and attack in a turn. So what do you think happens?
Just some thoughts :D This is a great thread, thanks for starting it Kyrt!