Button with Drupal Behavior jQuery Conflicting with AJAX 'Add More' Button on Unlimited Cardinality Field
So I went with a different approach to achieve the same thing. Instead of adding a button using the '#button' or '#submit' property in hook_form_alter, which was causing the conflict, I added a button with the following code:

$form['field_starting_weight_garbage']['und'][0]['value']['#prefix'] = '&lt;div&gt;';
$form['field_starting_weight_garbage']['und'][0]['value']['#suffix'] = '&lt;input type="submit" value="No Change" class="form-submit" id="garbagenochange"&gt;&lt;/div&gt;';


&amp; adjusted the Drupal Behavior to attach to this element (id="garbagenochange").

I still don't know exactly what was causing the conflict or how to fix it, but this does what I need, so I'll go this route.