Use Soliloquy image as a background slide instead of regular image.

gistfile1.php

<?php
add_filter( 'soliloquy_output_item_style', 'add_soliloquy_bg_image', 10, 4 );
function add_soliloquy_bg_image( $style, $id, $image, $idata ) {
	$style = 'background-image:url(' . $image['src'] . ');';
	return $style;
}

add_filter( 'soliloquy_output_image_slide', 'remove_soliloquy_slide_image' );
function remove_soliloquy_slide_image( $imagehtml ) {
	$imagehtml = '';
	return $imagehtml;
}

Hey :) Please remember, by removing the images from the slider, the main container (the list item) may not be able to calculate the height so you may have to add some custom CSS to add a height to your list items like this:

ul.soliloquy-slider li.soliloquy-item { height: 400px !important; background-size: cover; }

By using the background-size: cover; you're automatically telling Solioquy to have the background image stretch to fit the width and height of the container! :)