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Are you really committed to going? I found this to be a hot, crowded, exhausting day of waiting and lines, and the main attraction was a disappointment to me. The N'Stein tour was only about 30 minutes, and I read recently that some of the areas are closed for renovation. Obviously, you can research this. Is St Mary's Bridge open now?
Yes there will be crowds and crowds, no matter the day of the week.
Are there tickets still available? Perhaps your checking the website will answer your questions.
If this is your dream, obviously you must do it, but it is alot of work.
Have a great trip! Safe travels!