Hey Phil,
Drew Z converted his 540 Touring to a 6-speed (the donor was a wrecked 540i Sport), essentially the same swap you are considering. Others have done it as well. It's not cheap, but you are really talking about the difference in cost between repairing/replacing your auto tranny (which you will have to do anyway) and installing a 6-speed.
Your ZF 5HP30 auto tranny would be replaced with a 6-speed manual, an entirely different beast made by Getrag ("Type D"). You will have to find a wrecked donor car or a salvage yard that has the correct unit from an E34 540, an 840, or--I think--an E39 540.
Yes, there would be a lot of labor involved. Since you would not do it yourself, I'm guessing that it will ultimately prove prohibitive cost-wise: you might do better to bite the bullet and fix your auto tranny, then sell the car and buy a 6-speed car instead, without the headaches of arranging the swap.
It may only make sense to do this swap where the 6-speed is otherwise not available (like this
7 Series or Drew's Touring).