As it sounds like you cannot magically get a 3rd tank, I suggest 2 tanking it.
My guild when progressing this fight had a lot of issues at the exact same place you mentioned. What we ended up doing was placing World markers at the Auction House, The Inn, the hut closest to the entrance of Orgrimmar, The Bank and the Warchief's House.
Our tanks would start tanking the bosses, swapping every 5 stacks at the Warchief's House untill a Toxic Storm spawns close to the tanks and then move the boss to the next world Marker. We continue like this, and will never corner our selves up at the entrance to orgrimmar. Still after many months of killing this boss, if we bring him up to the gates we are likely to wipe. Move from Hut closest to the Entrance of Orgrimmar directly to the bank.
Mark one of your healers and tell all the ranged DPS to stack on him, he will position him self behind where the tanks are moving. If your tanks are at Auction House the Ranged camp will be somewhere between Warchief's House and Auction House, but not between Auction House and The Inn. Melee will be on Haromm and will only have to worry about the Foul Stream(?). This will make the road ahead of tanks clean and easier to handle.
When you get Slimes, the tank who is current agroholder on Kardris will move away from the raid, and spawn them so that they will not spawn on the tanks nor go through the raid. Say you are currently tanking at The Inn, I would usually then go between the inn and the Auction house or between the Inn and the Hut close to entrance of orgrimmar and spawn them. Your ranged DPS needs to focus the slimes down as soon as possible. Having your hunter chose Barrage Talent and save it for this situation will make things easier, but will still require more dps then that. If you do a tank swap during Slimes, the slimes will be spawned on the tank who taunted, so be careful.
I am sure you have figured out how Ashen Walls work, but I am going to explain it a bit still, just in case you are unsure. The current agroholder on Haromm will get a wall spawned from Shoulder to Shoulder, so Ideally you would place these inside houses or the entrances to buildings in general. or close to the wall of orgrimmar, out of the way of anyone. When Haromm starts casting the Ashen Wall he will stand still, and you have about 2 seconds to reposition your self. Ideally you would delay a tank swap till the wall has been placed, unless there is more then 5 seconds till the wall is about to be casted, so the new tank is able to position him self. This will likely be where you need to practice, this fight can be very stressful for tanks, so if need be have one of the less stressed players in your raid, one who feels more confident about the abilities to call out abilities like Slimes or Ashen Walls, so that you can do a splitsecond choice between tankswapping or keeping it for a while longer. Even when this fights become a rutine, it will be a bit stressing for you as a tank, so try to keep calm
at 25% use Bloodlust and keep your cooldowns running as much as possible to relieve your healers of some stress. Call out for outside Cooldowns if necessary, like Pain Supression, Ironbark, Vigilance or Hand of Sacrifice(?).
if you are not using Voice Communication, this fight will be a lot harder to coordinate, both for tanks and the healers.
greavous, please make another thread if you seek advice for shamans. It gets confusing for you and others to find the right answers when some people just read the 1st post and not the 3 pages of posts, while others read most of the posts and reply to your latest question.