(Note to other readers: The question author and I have already discussed via chat, so I'm going straight to the code.)
I think for performance reason, you should do it this way:
// FIRST PART: Get the variations which are in stock.
$paged = max( 1, get_query_var( 'paged' ) );
$wccaf_depth = array( '19', '1' ); // example
$args = array(