I cracked the top of my 2007 Schwinn 1 1/8 fork black label steerer tube.
What kinds of repair are available? Should I just buy a new name-brand carbon fork, e.g., Canondale, GT, Trek on ebay?
The standard line from the carbon repair shops is they don't do forks because new ones are a lot cheaper. My understanding is that safe steerer repairs are technically possible in a lot of cases, so if you want to go nuts or if the original is unique in some way you might be able to find someone to do it, but it's probably not worth it. I think in practical terms, the real problem is that a lot of the time if one part of a carbon fork is destroyed, the rest might be pretty well-loved also.
The usual approach is to measure the axle-to-crown and offset dimensions of the original and go shopping for something close. Among carbon rim brake road forks, there's not a lot of variance. A number of companies make what are essentially repair forks for this kind of situation.
Without meaning to rub things in, this is a good reason to invest in a torque wrench, as all components these days can be damaged from over-tightening. I've done this to a light aluminum seapost, so if you damaged the fork by hand-tightening, you'd be far from the only person. Depending on how much is damaged and how your stem and spacers are set up, it's possible you could trim the steerer and then flip the stem to get your original position. A simple bike geometry calculator is here.
Note that if you cut a carbon steerer yourself, you would need a mask and the appropriate cutting blade. That may be better left to a bike store. If you cut into the steerer and you see any voids in the carbon, that means the damage extends further down than you thought. In that case, it might not be an economical repair.
Speaking of the recommendation to find a fork with the same or similar rake and axle to crown distance (that's fork length, or parameter #3, in the site I linked to), that site would enable you to see how much the trail and position change if you got a fork with similar but not identical measurements.
Should I just buy a new name-brand carbon fork, e.g., Canondale, GT, Trek on ebay?
The definition of insanity is doing the same thing over and over again and expecting different results.
If you observed a certain material to be inadequate for a fork steerer tube, why are you going to purchase a new fork having a steerer tube made of the same material?