With more experimenting, I changed the radio button section to the following:
<input type="radio" name="PublishGroup1_<?php echo $RepeatSelectionCounter_1; ?>" value="1" <?php if (!(strcmp($row_css_selected['publish'],"1"))) {echo "checked=\"checked\"";} ?> id="PublishGroup1_0_<?php echo $RepeatSelectionCounter_1; ?>" >
The buttons behave as they should, however, when clicking submit, it adds '1' to ALL the records, rather than just the one selected.