Theming two Drupal aggregator blocks separately

Question

I'm fairly new to Drupal but have played with it for a while now - but this one's stumping me:

I've got two aggregator blocks on a site that I'm currently building. Is there a way of theming the whole block? Secondly, is there a way of theming the whole block depending on which aggregator it is?

I can theme individual items through theme_aggregator_block_item. However, this themes items within both of my aggregator blocks. I'd like a different output for the items depending on which aggregator it is.

I've tried the block-aggregator.tpl.php approach but any changes I make within that file do not get reflected (even after clearing cache). I'm putting this file in my theme directory and my theme directory/templates (just to make sure) and still getting nowhere. Other things are being overridden when I place them in this folder. Also, I can't see how this would enable me to theme one or the other.

I'm imagining that it's possible with a if($block_name_var == 'aggregator 1') { // do this } type approach but I cannot seem to get the block template to theme it in the first place.

Any thoughts or ideas would be appreciated.