Custom contributor attributes were added to the REST API in 4.0.3, in the "itemExtensions" property of the workItem element.  If you are on an older version than 4.0.3, I don't think you have any options.  Assuming you are on 4.0.3 or later, you can use a query such as:

https://HOSTNAME:PORT/CONTEXT_ROOT/rpt/repository/workitem?fields=workitem/workItem[id=1234]/itemExtensions[key="YOUR_CUSTOM_ATTRIBUTE_ID"]/value/itemId

to retrieve a pointer to the contributor object (replacing HOSTNAME, PORT, CONTEXT_ROOT and YOUR_CUSTOM_ATTRIBUTE_ID with the appropriate values).  This query scopes the results to only workitem 1234 but you can modify that as required.  Then a query such as

https://HOSTNAME:PORT/CONTEXT_ROOT/rpt/repository/foundation?fields=foundation/contributor[itemId="ITEMID_RETURNED_IN_FIRST_QUERY"]/emailAddress

to retrieve the users email address.  Note you could also replace "emailAddress" with "name" or "userId" depending on what you want to include in your report.

REST API documentation can be found here:
https://jazz.net/wiki/bin/view/Main/ReportsRESTAPI