Hi nycL45,
I thought about doing it with a 2 step array. If you have the curve that revolved the bowl you could do a curve array of the first hole to get the orientation, then do a circle array to fill the bowl.

Though a single circle array would produce multiple bottom center circles and you would have to edit them out, I did this with 3 steps, thinking you would not want the holes to be symmetrical I was going to suggest doing a second curve with a new set of holes at a different interval then rotate it a bit to get the random holes.

I noticed you demoed a symmetrical set of holes, so I will need to fool with this a bit to see if you can make the numbers add up to be symmetrical.