I think your understanding is exactly right.
With the transfer case acting like an open differential, it will spin the rears unless you get that ABS fixed. (or some other mod like welding)
Here is some more info on how that NV125 TC works, copied from the attached PDF article:
x5 transfer case tech article.pdf
"How does 4WD work?
The first transfer case used in 4WD BMWs was the New Process NV125 unit. The main component of the NV125 is the planetary gear set. This is what divides the torque to the front and rear differentials.
Here’s how it works: The transmission output shaft drives the entire planetary carrier, which provides a 68% rear/32% front torque split between the drive shafts. An annulus gear driven by the carrier directs power to the rear drive shaft. Sun gears in the planetary gearset transmit torque to a drive chain that then drives the front axle drive shaft.
This is a very strong design that is usually trouble-free. A key benefit is the ability to split torque under varying conditions thanks to the ADB (Automatic Differential Brake). When the DSC control unit senses a loss of traction based on input from the wheel speed sensors, the brakes are pulsed on the wheel that is spinning. This pulsed braking directs more torque to the other wheel on the same axle. If both wheels on the same axle indicate a loss of traction, the DSC module applies hydraulic pressure to both wheels so that torque flows only to the other axle. This original system is simple and sturdy."
BTW, that has a common typo - the actual split is 62:38, not 68:32. That split ratio is a direct result of the geometry of the planetary gearset in there, i.e., the relative sizes of the gears used.
And hey, I just had an idea that may have helped you in that situation - parking brake
