I am not sure if you can or cannot amend after 3 years period. When you sign the form under prejury of pentaly that means you acknowledge what you are doing. But still you can be misinformed and filled out the wrong form. Tax is very complex as we will know. there are too many pages to stay on record. So you could have made an honest mistake and write that as a reason you are amending the money on 1040X. 

I don't think you are required to show more than 3 years of your tax record. But since the laws are changing so rapidly who knows there will be an exchange betn. those two's databases. both are feds. ...

It's all upto you though..