I am not familiar with the I-20 form, and it does not look I can download it (with the exception of a sample document). This means, I don't know what would be allowed in the form. Here is what I would do (assuming, the form does allow you to do all these steps):
If that does not work, I would try the following
Write a script that will identify parts of the document that are close to where you need to add information to the form. Then programatically add annotations (e.g. a text annotation) with the information you need to provide in the correct location. This again could be triggered via a menu item.