Hi, Shane.
WooCommerce and Jetpack should run just fine together.
Do you have anything in the error logs to show us?
Try increasing memory to see if it still crashes as a test.
Add this to the top of wp-config.php to increase WP memory:
/** Memory Limit */
define('WP_MEMORY_LIMIT', '256M');
define( 'WP_MAX_MEMORY_LIMIT', '256M' );