A query endpoint might want to have different timeouts depending on whether queries are from untrusted or trusted users, or maintenance processes. The timeout could be passed with an X- header, a Timeout header as per http://tools.ietf.org/html/draft-loreto-http-timeout-00, or a query parameter, respecting the system default if none is provided. The query parameter might be less favourable as it'd be harder to filter out for Fuseki instances behind Apache.
There is a risk that changing the behaviour to allow timeouts to be overridden will lead to DoSs of query endpoints open to the world to some extent. This can be mitigated by defaulting to disallowing timeout overrides.
I'm happy to put a patch together and document it at http://incubator.apache.org/jena/documentation/serving_data/.