Yes, you can spin an alternator too fast. But as you sort of figured, it's not likely that you're getting to that point. Unless your particular alt just didn't like getting up into the 13k range that is.
The way I understand it, each design would be diferent (different case sizes, heat dissipation properties, bearing diameters and designs, stator size, etc.) and have different specs. And perhaps more powerful alternators (with larger components and electromagnetic fields and more stress on the bearings and heat output?) can't handle quite as much as smaller ones? So perhaps some brands (whether O.E. new or aftermarket rebuilts) just can't handle as much as others can.
Still, at 16k for a 3G like RedLeg was saying, you'd be within it's limits with your 2to1 ratio and ok with some brands, but maybe getting close to other's limits.
For those reasons, you might want to verify your pullies exact size, just so you can determine actual shaft rpm at the alt, so that nobody can give you any grief when you try to warranty another one.
Might just be good info to know since you're competing too.
And now that I think about it, if you're racing, you'd want your alternator spinning slower than normal anyway. Higher ratios for normal driving put out more power to keep things charged and running, but take more HP to drive. Lower ratios for racing around keep the shaft slower and waste less HP.
Not only would you lower your alt's stress, but gain hp at the same time. Bonus!
In the old days, when we'd drag race our cars (or dad's cars) at the track, an old timey trick was to disconnect the alternator entirely. Some would pull the belt, others would just unplug the wires from the back.
Hey, anything that would help in a pinch! We were just learning and the aftermarket was playing catch-up.
Good luck with whatever you're doing.
Paul