I was entirely referring to Garrosh N but was more an anecdotal refferance. Solo tanked it twice but never got the crane and people were questioning how to deal with the red crane transition before, especially for groups not having a warrior dps for in your case die by the sword. Out ranging makes it viable regardless of group setup.
As for Garrosh HC. The transitions are not random. You will never get the crane transition on Garrosh HC. Only part of the fight that actually requires two tanks is P3 entirely due to Empowered whatever the DoT is called. When the DoT explodes the damage would kill your raid in Heroic in P3. The other issue would be the second transition which could show to be a problem depending on what tank you got. I would not like to solo tank on a paladin as aggroing all the adds would be an issue. A warrior could do it without issue however. Having a paladin (ret or holy would not matter) would siginificantly help though.
Now, I am probably talking a bit conservatively here as my experience of Garrosh is having the "correct" gear for it. If you have a raid team average ilvl of 575 or higher, I think it is highly possible that going with 1 tank 1 healer, you would only get 1 transition in P2, so the second transition is not a problem.
You would also for sure only get 1 EWC in P3, maybe 0. If you can get away for 0 EWCs in P3, and maybe even 1, you could just chain all your defensives and raid CDs for it to survive it.
So really, I guess garrosh HC is solo tankable with enough gear to get 1 P2 transition and 0-1 EWCs in P3.
We had about 566-568 average ilvl when we killed garrosh and I believe our record before the second transition was 16%, with 18-22% being average. Dropping a tank and healer for another dps, and for sure getting 5-10 more item levels on the group would make pushing those last 6-12% trivial.