There is actually a very simple method of handling this:
1.5-2 seconds after Black Obtuse is done casting, have the tank taunt. He will get hit for a moderate amount that would have otherwise gone to someone else but no one else will take damage. I tank this with a sin and after datacores are down, he respecs dps and i solo tank all of phase 2. I only mention that to show you that once your tank learns how the mechanics operate, its basically a 1 tank fight. The only thing to keep in mind is that if you tank gets targeted for deletion, which happens a lot now, he does like to drop aggro, so save aoe taunt for those occasions.
Ive seen other people use 2 tanks for it. 1 tank taunts right before black obtuse is ending and the other tank taunts right after the cast is done. This will cause the first tank who taunted to take the hit instead of a dps/healer.
Hope this helps clear up some issues.
You have a tank respec midfight, with all the stuff going on? Does he change all his gear too? And thats on a fight which has a very very loose enrage timer. Either your DPS are bads or your co tank is trying to be snazzy. There is absolutely no need to respec midfight.
Does he do it for the 4th boss too? as after 50% its a 1 tank fight.