You don't need to worry too much about Musashi as she will come back. Basically, if the Summon schedule is the same, King Hassan comes after Musashi, but Musashi will come back when Shimousa comes out. If you wish for Musashi, but want to focus on King Hassan, you can wait until Shimousa for Musashi.
Or if you are willing to test your luck with your money, there is a Lucky Bag Summon Banner between Musashi's First Banner and the Shimousa Banner where you can use Paid Quartz to get a random, but Guaranteed 5-Star Servant and among them includes Musashi. Note that you cannot use Free Quartz on those Lucky Summon Banners and you must use Paid Quartz, so saving up Free Quartz for those Banners won't help and that you must wait until Shimousa if you wish to use the Free Quartz to try and get Musashi the 2nd time.
That being said, if the Summon schedule is the same, Edmond Dantes actually comes back after King Hassan. Poor you.

But like Musashi, he can also be gotten from one of the Paid Quartz Banners later on.