There are some options. Yes, a carbide drill bit will drill thru the extractor bit. Don't be fooled by "Titainium Carbide" coated drill bits, they will not help you any. Cobalt drills, marked "CO" on the bit, are also harder, but depending on the style of extractor, may not be hard enough. Call a machine tool business and see if they have what you need. You might also consider picking up a diamond burr bit for a dremel tool and using that to grind a divit as close to on center as possible, this will help you drill on center. Slow rpm, and don't apply too much pressure, but you need as big a hole in the bolt as you safely can, even if you need to drill in stages, going up a size after getting a nice small hole in there. And don't whack the piss out of the extractor when you put it in, or it runs the risk of spreading the bolt remains in the hold, jamming it even tighter against the aluminum threads of the hole.
I just did this routine today on a pressure washer, but got lucky and the broken piece, snapped off just below the surface of the aluminum head, was loose and came out easily. That type of break is vibration related. And a real pain. I replaced the bolts with studs, where you have a short end and a long end, with a shoulder in between. The short end goes into the hole and bottoms against the shoulder. Depending on your rack, this may be an option for you, going to studs rather than replacing the bolts again.
If all that fails...
You may need to find someone with a EDM machine to burn it out. Essentially it arcs with a special electrode that is hollow with coolant running thru it and 'burns' the bolt out. Will go thru hardened taps too. You're going to need to remove the subframe from the bike for that, and find a machine shop that does that type of work. But, at that point, you could toss it on a mill and use a carbide center cut end mill and just machine most of the bolt out, then pick out the remaining pieces. It's time consuming and precise work. (I'm a machinist, btw, and have done this many times, as well as the EDM for broken taps.)