Wordpress - How to echo the_excerpt without the P tag wrapper?

in your code above use get_the_excerpt() instead of the_excerpt(), because the last one will output the excerpt to the screen, and not pass it to your other functions...

What about removing the wpautop filter before your list?

remove_filter( 'the_excerpt', 'wpautop' );

(Make sure to add it back afterwards, so as not to mess up other formatting...)