That sucks. Sounds like you have a solution that is acceptable to you, so I wish you godspeed.
For your future action, or for those learning in this thread, backing out snapped bolts can be done as related above by drilling a small pilot hole in the bolt and using an easy-out bolt extractor. As stated by the former AF maintainer, the key is to drill the center of the bolt. This should be done by first using a center-punch to dimple the center of the bolt. This will locate the drill bit, else the drill bit will 'walk' on you. Use WD-40 or other spray lube to spray the drill bit every few seconds when drilling the bolt; this cools the bit and bolt material and the lubrication greatly eases the cutting. It's easier to do than it sounds.
Anti-sieze is usually a good idea with two dissimilar metals but I dunno what BMW's policy is on anti-sieze, and keep in mind it will change your torque values as torque specs do not account for the lubricity of anti-sieze.