Thanks for your response, Francis!
I don't have complete control over the client (coworker), but inspecting the header, that was in fact the case. I tried switching to using proxy_pass and proxy_request_buffering instead of the uwsgi module, which doesn't have quite as harsh of a limitation...
"""
When HTTP/1.1 chunked transfer encoding is used to send the original request body, the request body will be buffered regardless of the directive value <i>unless HTTP/1.1 is enabled for proxying.</i>
"""
I enabled proxy_http_version 1.1 as the docs suggest, but still no go. I'll keep whacking at it for a while before finding another route. Will post back if I come up with a working solution.