I had to file for one of these back in April -- at first I tried by phone, and fax, and got no response.
Then I filed one electronically, and that seemed to work the best. There was definitely an upload button when I went through it because I included a letter from a doctor. I was using Safari. Here are the steps I followed (sounds like you've done the same):
- On the united website, go to Refunds, under the "Reservations" drop down menu
- Choose e-ticket refund as the type
- Towards the bottom there is an "upload additional documentation" section
- choose your file
- after filling out the other parts of the page, click continue.
I think that the upload is automatic, but could be wrong.
In the end, that portion of the ticket was refunded, and no $50 processing fee was charged (maybe because I politely mentioned the hassle involved with filing one of these claims

).