Heh, funny. I'm using just the opposite grip that is suggested in the article for right handed people. Article says to grip dominant hand under and the other hand over and I'm just the opposite.
But are you sure it's no use to alternate grips? Would make sense to alternate every now and then..
Why though? I mean if I'm wrong someone can feel free to correct me, but I can't imagine what the benefit would be. Alternate grip is just used for your heavy weight, and you should transition away from it as you get heavier.
For example, I used to alternate on 225. Now I overhand that in my warmups, but alternate 315. By the end of summer I'd like to overhand that with chalk.