I have somewhat of a mess on my hands with a certain file. So I was given a (.ai) file by a client that contains 20,000 circles (210 circles high by 90 circles wide where each circle needs to be labeled with a different letter (that corresponds to a pre-agreed upon color scheme) to indicate what color the balls will be in real life when this file is turned into a physical art piece. 

So, I have already labeled each circle with the correct letters, but since this file is going to later be used by a cnc cutter to etch the letters into the bottom something of a half-dome/cup-like shape (in wood) I am told each letter needs to be EXACTLY in the center (horiz and vert) of each circle in order for the cuts to come out correctly. Currently, they are not perfectly centered.

Is there a quick, easy way to select all the letters (and/or maybe all the balls?) and 'tell' illustrator to space them all out in a perfect grid to match up to the balls (the balls are perfectly spaced, but my placement of the letters within them is unfortunately not)?

The only thing I can think of so far is to center-align each line....line-by-line....which is taking AGES and I have a tight deadline. Surely, there has to be a better way that I am ignorant of?