The strap goes into a horizontal, oblong slot below and perhaps very slightly forward of the alternator ear.
I use a stainless steel eyebolt of the proper length and diameter. It won't bend like the soft steel eyebolts. Never a problem:
Thread a nut all the way onto the eyebolt, until it runs out of thread. Slip a flat washer on. Slip the eyebolt, nut and flat washer through the alternator eye. Follow up with another flat washer, a lock washer and a cap nut. Tighten. All the hardware, all of it, should be stainless steel.
The strap stays on all the time, not just for racing.
One possible reason for breaking the alternator is a hard launch with the strap loose. That will shock load the alternator. Check that your strap is snug, but not excessively tight, at all times. Buying a good strap, not a cheapie that will loosen up routinely, is a necessity. Also, a good niylon strap has just the right amount of "stretch" to keep your alternator healthy.
If you don't want to take this amount of precaution, then most certainly go get the motor mount.