Why not start with a template which has one little circle with a placed image clipped inside of it. Now, all you have to do is relink the image to have the new picture appear in the circle at the smaller size. Then use the Live Transform effect on your one circle to create your grid of circles.
To use Live Transform effect - select the circle group and apply a transform effect with a horizontal move and some copies. Then apply the same effect again, this time with a vertical offset and a number of copies.
In this image, I have this applied to a path, but this can be applied to a group containing a clipped placed file too.
Using a library of graphic of styles you can have all sizes of step-&-repeat accessible via click in a list view.
This is great for setting up the grid, however I am having issues "recording" the transform effect action. I want to automate this for future use. What am I doing wrong?
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You have to save your transforms in a graphic style and an action can apply the graphic style of a particular name that is present in the document.
To record a live effect into a graphic style, use Window > Graphic Styles to use the graphic styles panel.
If you have several different transform configurations, and do not care for the entire library of transform graphic styles to be present inside your active document, you can build into your actions an action which copy/pastes from a file all artwork, and you can have the graphic styles attached to this artwork - it will make them appear in your document you're pasting into.
Such an action to fetch styles will need to open a file, select all, copy, then close active file, then do paste to paste into the file that was originally open, then do delete to remove the pasted artwork - the styles stay in the document.