This page suggests the following PHP config change:
max_input_vars: When files are uploaded via HTML5 drag and drop file upload APIs, PHP parses the file body as though it contained normal POST parameters, and may trigger max_input_vars if a file has a lot of brackets in it. You may need to set it to some astronomically high value.
This seems like a really silly and inefficient workaround, when disabling enable_post_data_reading would probably also fix it. I wasn't sure if Phabricator would be okay with it, but @epriestley's comment on T4369 seems to indicate that it would be fine.
If this would work, the docs could be updated to describe the better solution.
If this wouldn't work, perhaps some code changes could be made that would fix any issues. I'd possibly be willing to dive in and do it if someone points me in the right direction. :)