I'm impressed, most the the chain gang ABS FAQ I wrote back in about 2000 is still there! Glad they improved the pictures though, mine were rubbish.
The spongy feel is NOTHING to do with ABS function. The BMW instructions about the diagnostic tool is related to the fact that they employ rough arsed fitters who don't have a clue who need to look for the bits they broke. The fastest way to find an ABS fault is via the diagnostics, especially when you need green=good, red=bad level screens!
Boy, didn't realise I was still so cynical. Best get it over with; IMHO Alan Jeffries BMW in Shipley West Yorkshire UK couldn't find an electrical fault if you gave them Farraday, Einstein and Bill Gates' entire staff to help
Pull the fuse and the four ABS solenoids (two hold, two release for each wheel) spring fully home and you have a conventional, fully effective brake system with exactly as much air in it as before. If they didn't spring back under the 40-100 bar you can apply you'd have a lever you couldn't pull back or one that felt like it had no fluid at all. You'd also have a red light on. A sensor fault is harder for the electronics to detect, but would result in ABS cyling (ie big lumpy brake modulations on a BMW) not a smooth but soft feel.
The problem here is almost definately air in the system. As it remains after the usual bleed procedure you have a leak. The leak might be where the hoses pass through the ABS module, but there is nothing electrical wrong it's going to be a loose pipe or similar. You want to run over all the Banjo's and hoses IMHO. Bleeding via a pump is a lot easier with ABS as there are nooks and crannies in the solenoid block, but enough pressure and/or patience will give results. Holding the lever back overnight works well too.
If BMW decide to charge you a fortune to do anything related to the ABS to fix this, I'd point out it isn't rocket science/brain surgery/black magic and whatever they replace it had better fix it. For some weird reason they always start by replacing the expensive bits
I've not touched a BMW since the incident with the F650 water pump impeller/head gasket in the middle of Morocco, but please feel free to contact me off line if you think I can help.
Good Luck
Andy