I agree with Graham's suggestion as being the most elegant. It will be a matter of identifying the spot in the documents you want the information stored. These may well have bookmarks already if they are legacy Word forms.

A less elegant solution would be mail merge, but that would require that on some level you have the ability to edit the forms you are filling in to turn them into primary merge documents with merge fields. Mail merge requires less technical ability than does vba for a userform, IMHO. However, getting permission to alter government forms (even if not changing layout or text) may require more than you can deal with.

Note, I regularly modify non-modifiable government forms to make them mail merge, but I don't work for the government. If what they want is the paper result, it shouldn't matter to them.