Thank you all for the advice and help.
Eventually I decided to take the K1200LT to a local repairer in Nottingham who specialises in BMW motorcycles (not a dealership).
I had a lengthy discussion with him as he knew all about these ABS units and their unreliability. He had changed many of these units on a range of BMW bikes and costing over £1500 for each repair. He said there was no guarantee that the same failures would not re-occur after spending this obscene amount if money.
His professional recommendation was to remove the entire unit and 'normalise' the braking system.
This entailed a small pipework and electrical modification to the bike.
Obviously you lose the ABS facility and the integrated braking but you do end up with a reliable and good braking system.
Obviously I was concerned about braking performance, residual value of the bike with this system bypassed, insurance implications etc. but in the end I decided to have the system removed and normalised.
The bike rides great, the new brakes work fine and I am very pleased with the cost of just £235 for the work, including an MOT test - ensuring the brakes are up to regulations and performance.
I also have peace of mind that the braking will be reliable as the complexity of the system has been simplified.
As for the effect on the re-sale value of my bike if I ever decide to sell it on... well I hope common sense prevails. The bike will be more reliable and future owners will not have the threat of an expensive ABS failure in the back of their minds. I have also kept the ABS control unit that could be potentially repaired and re-installed in the future if the new owner wished to do so.
I love my K1200LT anyway and I will probably never sell it until I'm too old to be able to keep it upright
Again, thanks for everyones help and advice and I hope my experiences will help other owners in the same predicament.