一定不用shall,你看错答案了吧,选should
A、此题主句是过去式,要用也用might,不会选may
B、shall只有两种用法：①用于一二三人称的疑问句,表示征求意见如Shall I open the door?
②用于二三人称陈述句,表示威胁警告命令.如You shall do as I say.
C、看句意：那时候我有可能去美国,如果用might那么句子应该改成It was possible that I might in America at that time.
D、句型“It is/was+natural/right/necessary/important/no wonder/possible等+ that从句”中,从句谓语常用should+动词原形
所以选D最准确
希望能帮到你^_^