Unless I am missing something, it will be impossible to get Mid-Autumn Sai

We can get up to 10 frags per day from lanterns. 10x7 = 70

Also there is a drop chance for one frag from those moon cakes. We can get 7 cakes through entire event. Even if someone is extremely lucky and gets frag from every cake, that's 77 frags from event. 3 short.

There is no possibility to buy either cake or more tickets to play lanterns game nor there are frags for him in any other event this week.