How can I get copies of library of congress's archival manuscripts?
This is not an answer, but too long for a comment.

I used to live around Washington DC metro area. I went to Library of Congress very often. They don't have open shelf policy. You sit in one of their reading rooms and pick a desk. You request for materials to read. The librarian will find them and put on a cart. Somebody moves the cart out to the desk you sit. After you finish, they'll put them back to the shelf. I never checked out books from them. Don't know their check out policy.

I remember there was a certain limit number of books for the request. 5 seems to be correct because you can only load a certain number of books on the cart.

It is definitely worth while to ask a Congressperson to help if you live in the US. But, it sounds like it's worth making a trip there to examine everything they have. 106 boxes is a lot. It takes half a container. I am afraid no libray is willing to take such a huge task - I assume you're thinking of inter-library loan. My 2 cents.