Husband and Wife, two passports - Category L - Entries - M

Question from USA. Thank you in advance for answering our question. We traveled to China in October 2014. We plan to take a cruise in April 2015. Our Visas show: Enter before - 22Jul2015 and Issue Date 22Jul2014. On April 7, we will stay in a hotel in Hong Kong for two nights. Four days later, we will be in Taipei, Taiwan...will sleep on the ship, but would visit Taipei for two days. A week later, we will still sleep on the ship, but will spend three days in Beijing. We disembark the ship in Shanghai and plan to spend a least one night in Shanghai before returning to the USA. From what I have read on your site about our passports, it appears that we satisfy the Chinese entry permits requirements with Category L - Entries - M. Are we going to be fortunate to be able to use these entry permits once more? Thank you very much! Bonnie and John